Abramowitz, M. and I. Stegun

[I] Handbook of Mathematical Functions, N.B.S. Applied Math. Ser. 55 (1964), Washington, DC.

Adams, J. C.

[1] On the expression of the product of any two Legendre's coefficients by means of a series of Legendre's coefficients, Proc. Royal Soc. London. 27 (1878), pp. 63-71.

Aharonov, D. and S. Friedland

[I] On an inequality connected with the coefficient conjecture for functions of bounded boundary rotation, Ann. Acad. Sei. Fenn. Ser. AI, 524 (1972).

Alexander, J. W., II

[1] Functions which map the interior of the unit circle upon simple regions, Ann. of Math., 17 (1915), pp. 12-22.


Orthogonal expansions with positive coefficients, Proc. Amer. Math. Soc., 16 (1965), pp. 1191-1194.

Mehler's integral for Pjcos 8), Amer. Math. Monthly, 76 (1969), pp. 1046-1049.

Orthogonal polynomials and positivity, Studies in Applied Mathematics 6, Wave Propagation and Special Functions. D. Ludwig and F. W. J. Olver. eds., SIAM, Philadelphia. 1970, pp. 64-85.

Linearization of the product of orthogonal polynomials. Problems in Analysis, R. Gunning, ed., Princeton University Press, Princeton, N.J., 1970, pp. 223-228.

Orthogonal expansions with positive coefficients. II, SIAM J. Math. Anal., 2 (1971), pp. 340- 346.

Positivity of the Cotes numbers for some Jacobi abscissas, Numer. Math., 19(1972), pp. 46-48.

Positive Jacobi polynomial sums, Tôhoku Math. J., 2nd ser., 24 (1972), pp. 109-119.

Mean convergence of orthogonal series and Lagrange interpolation. Acta Math. Acad. Sei. Hungar.. 23 (1972), pp. 71-85.

Griinbaum's inequality for BesseI functions, J. Math. Anal. Appl., 41 (1973), pp. 122-124.

Summability of Jacobi series. Trans. Amer. Math. Soc., 179 (1973), pp. 71-84.

Refinement of Abel summability for Jacobi series, Proc. Symp. Pure Math. vol. 26, Harmonic Analysis on Homogeneous Spaces, C. Moore, ed.. American Mathematical Society, Providence. R.I., 1973. pp. 335-338.

Certain rational functions whose power series have positive coefficients. II, SIAM J. Math. Anal.. 5 (1974), pp. 53-57.

Jacobi polynomials, I, New proofs of Koornwinder's Laplace type integral representation and Bateman's bilinear sum. Ibid., 5 (1974), pp. 119-124.

Some absolutely monotonie functions, Studia Sei. Math., 9 (1974), pp. 51-56.

Some characteristic functions of unimodal distributions, J. Math. Anal. Appl., 50 (1975), to appear.

Positive Jacobi polynomial sums, III, Linear Operators and Approximations, II, P. L. Butzer and B. Sz. Nagy, eds., Birkhäuser Verlag Basel, 1975.

Radial characteristic functions, Mathematics Research Center, Tech. Rep. 1262, University of Wisconsin, Madison.

A note on the history of series, Mathematics Research Center Tech. Rep. 1532, University of Wisconsin, Madison.

Askey, R. and J. Fitch

Positivity of the Coles numbers for some ultraspherical abscissas, SIAM J. Numer. Anal., 5 (1968). pp. 199-201.

Solution to Problem 67-6, A Trigonometric inequality, by J. N. Lyness and C. B. Moler, SIAM Rev., 11 (1969), pp. 82-86.

Integral representations for Jacobi polynomials and some applications, J. Math. Anal. Appl., 26(1969). pp. 411-437.

A positive Cesdro mean, Publ. Elek. Fak. Univ. Beogradu, ser. Mat. i Fiz.. 406 (1972), pp. 119- 122.

Askey, R.. J. Fitch and G. Gasper

[1] On a positive trigonometric sum, Proc. Amer. Math. Soc., 19 (1968). p. 1507. Askey, R. and G. Gasper

Linearization of the product of Jacobi polynomials. III. Canad. J. Math.. 23(1971). pp. 332-338.

Jacobi polynomial expansions of Jacobi polynomials with non-negative coefficients, Proc. Camb. Phil. Soc., 70 (1971), pp. 243-255.

Certain rational functions whose power series have positive coefficients, Amer. Math. Monthly, 79(1972). pp. 327-341.

Convolution structures for Laguerre polynomials, J. Analyse Math., to appear.

Positive Jacobi polynomial sums, II, Amer. J. Math, to appear. Askey, R„ G. Gasper and M. Ismail

[1] .4 positive sum from mmmability theory, J. Approximation Theory, 13 (1975). to appear. Askey, R. and H. Pollard

[1] Some absolutely monotonie and completely monotonie functions, SIAM J. Math. Anal., 5 (1974). pp. 58-63. Askey. R. and J. Steinig

Some positive trigonometric sums. Trans. Amer. Math. Soc., 187 (1974), pp. 295-307.

A monotonie trigonometric sum. Amer. J. Math., to appear. Askey, R. and S. Wainger

A transplantation theorem for ultraspherical coefficients. Pacific J. Math.. 16(1966).pp. 393-405.

A dual convolution structure for Jacobi polynomials, Proc. Conference on Orthogonal Expan­sions and their Continuous Analogues, D. Haimo, ed.. Southern Illinois University Press, Carbondale, 1967, pp. 25-36.

Atkinson. F. V.

[1] Discrete and Continuous Boundary Problems, Academic Press. New York. 1964. Bailey, W. N.

On the product of two Legendre polynomials, Proc. Camb. Phil. Soc., 29 (1933), pp. 173-177.

Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935.

The generating function of Jacobi polynomials, J. London Math. Soc., 13 (1938), pp. 8-11

Contiguous hypergeometric functions of the type sF2i I ), Proc. Glasgow Math. Assoc., 2 (1954), pp. 62-65.

Bateman. H.

A generalization of the Legendre polynomial, Proc. London Math. Soc. (2), 3 (1905), pp. 111-123.

The solution of linear differential equations by means of definite integrals, Trans. Camb. Phil. Soc., 21 (1909). pp. 171-196.

Partial Differential Equations of Mathematical Physics, Cambridge University Press. Cambridge,

1932. Beckner, W.

[1] Inequalities in Fourier analysis on R", Proc. Nat. Acad. Sci. U.S.A., 61 (1975), to appear. Bingham, N. H.

[1] Integral representations for ultraspherical polynomials, J. London Math. Soc. (2), 6 (1973), pp. 1-11. Boas, R. P., Jr.

[1] Entire Functions, Academic Press, New York. 1953.bochner. S.

Hilbert distances and positive definite functions, Ann. of Math. (2), 42 (1941), pp. 647-656.

Positive zonal functions on spheres, Proc. Nat. Acad. Sei. U.S.A.. 40 (1954). pp. 1141-1147. Braaksma, B. L. J. and B. Meulenbeld

[1] Jacobi polynomials as spherical harmonics, Indag. Math.. 30 (1968), pp. 384-389. brannan, D. A.. J. G. cwjnie and W. E. klrwan

[1] On the coefficient problem for functions of bounded boundary rotation, Ann. Acad. Sei. Fenn. Ser. AI. 523 (1973). Brown, J. W. and J. L. Goldberg

[1] Generalized Appell connection sequences, J. Math. Anal. Appl., 46 (1974), pp. 242-248. Burchnall. J. L. and A. Lakin

[1] The theorems of Saalschütz and Dougall, Quart. J. Math. Oxford (2), 1 (1950), pp. 161-164. Bustoz, J.

[1] Jacobi polynomial sums and univalent Cesàro means, Proc. Amer. Math. Soc., to appear. Carlitz. L.

On a problem in the history of Chinese mathematics. Mat. Lapok.. 6 (1955), pp. 219-220.

A formula of Bateman, Proc. Glasgow Math. Assoc., 3 (1957). pp. 99-101.

Some generating functions for the Jacobi polynomials. Bull. U.M.I. (3). 16 (1961 ). pp. 150-155.

The product of two ultraspherical polynomials, Proc. Glasgow Math. Assoc.. 5 (1961-2), pp. 76-79.

Carlson, b. C.

[1] New proof of the addition formula for Gegenbauer polynomials. SI AM J. Math. Anal.. 2 ( 1971 ). pp. 347-351. Cartan. E.

[1] Sur la détermination d'un système orthogonal complet dans un espace de Riemann symétrique clos. Rend. Cire. Mat. Palermo, 53 (1929), pp. 217-252. Chébli, h.

[1] Sur la positivité des opérateurs de "translation généralisée" associés à un opérateur de Sturm- Liouville sur [0. зо[. C.R. Acad. Sei. Paris. Ser A. 275 (1972). pp. 601-604. Cholewinski. F. M. and D. T. Haimo

[1] Classical analysis and the generalized heat equation, SI AM Rev., 10 (1968), pp. 67-80. Chrystal, G.

[1] Algebra, vol. 2, 2nd ed., A. and C. Black. London, 1900. Сни. Shih-Chieh

[1] Ssu Yuan Yii Chien {Precious Mirror of the Four Elements), 1303 (Chinese). Church, R. F.

[1] On a constant in the theory of trigonometric series, Math. Comp., 19 (1965). p. 501. Clausen. T.


ein Quadrat von der Form


[1] Lieber die Fälle, wenn die Reihe von der Form

hat., J. Reine Angew Math., 3 (1828), pp. 89-91. coifman. R. R. and G. weiss

[1] Representations of compact groups and spherical harmonics, L'Ens. Math., 14(1968),pp. 121- 173. Copson, E. T.

[1] An Introduction to the Theory of Functions of a Complex Variable, Oxford University Press. Oxford, 1935.

cornille, h. and a. martin

Constraints on the phase of scattering amplitudes due to positivity. Nuclear Physics, B49 ( 1972), pp. 413-440.

Constraints on the phases of helicity amplitudes due to positivity. Ibid., B77 (1974), pp. 141-162.

Davis, J. and I. I. Hirschman, Jr.

[I] Toeplitz forms and ultraspherical polynomials. Pacific J. Math.. 18 (1966). pp. 73-95.

Delsarte. P.

[I] An algebraic approach 10 the association schemes of coding theory. Philips Res. Reports Suppl., 10(1973).

Delsarte, P., J. M. Goethals and J. J. Seidel

[1] Bounds for systems of lines, and Jacobi polynomials, to appear.

Dinghas. A.

[I] Zur Darstellung einiger Klassen hypergeometrischer Polynome durch Integrale von Dirichlet- Mehlerschen Typus, Math. Zeit., 53 (1950), pp. 76-83.

Dougall. J.

On Vandermonde's theorem and some more general expansions, Proc. Edinburgh Math. Soc., 25(1907), pp. 114-132.

A theorem of Sonine in Besse! functions, with two extensions to spherical harmonics. Ibid., 37(1919). pp. 33-47.

The product of two Legendre polynomials. Proc. Glasgow Math. Assoc.. I (1952/3), pp. 121-125.

Dunkl. C. F.

An expansion in ultraspherical polynomials with nonnegative coefficients, SIAM J. Math. Anal.. 5 (1974), pp. 51-52.

A Krawtchouk polynomial addition theorem and wreath products of symmetric groups, to appear.

Dunkl, C. F. and D. E. Ramirez

[I] Krawtchouk polynomials and the symmetrization of hypergroups. Ibid., 5 (1974), pp. 351-366.

Durand. L.

[I] Nicholson-type integrals for products of Gegenbauer functions. Abstract in Notices Amer. Math. Soc.. 20 (1973). pp. 704-B24.

Eagleson, G. K.

[I] A characterization theorem for positive definite sequences on the Krawtchouk polynomials. Austral. J. Statist., 11 (1969), pp. 29-38.

Erdêlyi, A.

[1] Transformation of hypergeometric integrals by means of fractional integration by parts. Quart. J. Math. (Oxford), 10 (1939), pp. 176-189.

Erdélyi, A., et al.

Higher Transcendental Functions, vol. 1, McGraw-Hill, New York, 1953.

Higher Transcendental Functions, vol. 2, McGraw-Hill, New York, 1953.

Euler, L.

[1] Specimen transformationis singularis serierum. Nova acta academiae scientiarum Petro- politanae, 12 (1794), 1801, pp. 58-70; reproduced in Opera Omnia, 16 (part 2) (1935), pp. 41-55.

Favard. J.

[I] Sur les polynômes de Tchebycheff, C. R. Acad. Sei. Paris, 200(1935), pp. 2052-2055.

Fejér. L.

Sur le développement d'une fonction arbitraire suivant les fonctions de Laplace, C. R. Acad. Sei. Paris, 146 (1908), pp. 224-225; reproduced in Gesammelte Arbeiten, I, pp. 319-322.

Über die Laplacesche Reihe, Math. Ann., 67 (1909), pp. 76-109; reproduced in Gesammelte Arbeiten, I, pp. 503-537.

Einige Sätze, die sich auf das Vorzeichen, u.s.w., Monatsh. Math. Phys., 35 (1928), pp. 305-344; reproduced in Gesammelte Arbeiten, II, pp. 202-237.

Ultrasphàrikus polynomok összegt'röl, Matés Fiz. Lapok, 38 (1931), pp. 161-164; Uber die Summe ulträspharischer Polynome, reproduced in Gesammelte Arbeiten, II, pp. 421-423.

Mechanische Quadraturen mit positiven Cotesschen Zahlen, Math. Zeit., 37 (1933), pp. 289- 309; reproduced in Gesammelte Arbeiten, II, pp. 457-478.Gestaltliches über die Partialsummen und ihre Mittelwerte bei der Fourrierreihe und der Potenzreihe, Zeit. Angew. Math. Mech., 13 (1933), pp. 80-88: reproduced in Gesammelte Arbeiten, H. pp. 479-492.

Neue Eigenschaften der Mittlewerte bei den Fourierreihen, J. London Math. Soc., 8 (1933), pp. 53-62; reproduced in Gesammelte Arbeiten, II, pp. 493-501.

Trigonometrische Reihen und Potenzreihen mit mehrfach monotoner Koeffizientenfolge, Trans. Amer. Math. Soc., 39 (1936), pp. 18-59; reproduced in Gesammelte Arbeiten, II, pp. 581-620.

Feldheim, E.

On the positivity of certain sums of ultraspherical polynomials, J. Analyse Math., II (1963), pp. 275-284.

Contribution à la theorie des polynomes de Jacobi, Mat. Fiz. Lapok, 48 (1941), pp. 453-504 (Hungarian, French summary).

Feller. W.

[1] Infinitely divisible distributions and Bessel functions associated with random walks, SIAM J. Appl. Math., 14(1966), pp. 864-875. Ferrers, N. M.

[1] An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them, Macmillan, London, 1877.           »

Fields, J.

[1] Asymptotic expansions of a class of hypergeometric polynomials with respect to ihe order, HI, J. Math. Anal. Appl.. 12(1965). pp. 593-601. Fields, J. and M. Ismail

[I] On the positivity of some 's, SIAM J. Math. Anal.. 6 (1975), pp. 551-559. Flensted-Jensen, M.

Paley-Wiener type theorems for a differential operator connected with symmetric spaces. Ark. Mat., 10(1972), pp. 143-162.

The spherical functions on the universal covering of SU(n - 1, I )/SU(n - I), Mat. Inst. Kbhvn. Univ. Preprint Series, I (1973).

Flensted-Jensen. M. and T. H. Koornwinder

[1] The convolution structure for Jacobi function expansions. Ark. Mat.. II (1973), pp. 145-162. Folland, G. B.

[1] Spherical harmonic expansion of the Poisson-Szegö kernel for the ball, Proc. Amer. Math. Soc., to appear. Freud, G.

[1] Orthogonale Polynome, Birkhäuser-Verlag, Basel and Stuttgart, 1969. Fuchs, I.

Potenzreihen mit mehrfach monotonen Koeffizienten, Arch. Math., 22 (1971), pp. 275-278.

Power series with multiply monotonie coefficients. Math. Ann., 190 (1971), pp. 289-292. Gangolli, R.

[I] Positive definite kernels on homogeneous spaces and certain stochastic processes related 10 Levy's Brownian motion of several parameters, Ann. Inst. H. Poincaré. Sect. B. 3 (1967), pp. 121-226. Gasper, G.

Nonnegative sums of cosine, ultraspherical and Jacobi polynomials, J. Math. Anal. Appl.. 26 (1969). pp. 60-68.

Linearization of the product of Jacobi polynomials. I, Canad. J. Math., 22 (1970), pp. 171-175.

Linearization of the product of Jacobi polynomials. II, Ibid., 22 (1970), pp. 582-593.

Positivity and the convolution structure for Jacobi series, Ann. of Math., 93 (1971), pp. 112-118.

Banach algebras for Jacobi series and positivity of a kernel. Ibid., 95 ( 1972), pp. 261 -280.

Nonnegativity of a discrete Poisson kernel for the Hahn polynomials, J. Math. Anal. Appl., 42 (1973), pp. 438-451.

Projection formulas for orthogonal polynomials of a discrete variable. Ibid., 45 (1974), pp. 176— 198.

Positive integrals of Bessel functions, SIAM J. Math. Anal., 6 (1975), to appear.

Formulas of the Dirichlet-Mehler type, to appear.

Gegenbauer, L.

Zur Theorie der Functionen X", Sitz. Akad. Wiss. Wien. Math.-Naturw. Kl., 66 (2), (1872), pp. 55-62.

Uber einige bestimmte Integrale, Sitz. Math. Natur. Klasse Akad. Wiss. Wien, 70 (2), (1875), pp. 433-443.

Zur Theorie der Functionen C'Jx), Denkschriften der Akademie der Wiss. in Wien, Math. Naturwiss. Kl., 48 (1884). pp. 293-316.

Gilbert, R. P.

[I] Function Theoretic Methods in Partial Differential Equations, Academic Press, New York, 1969.

Gillis, J. and G. Weiss

[1] Products of Laguerre polynomials, M.T.A.C. (now Math. Comp.), 14 (1960), pp. 60-63.

Ginibre, J.

[I] General formulation of Griffiths' inequalities. Comm. Math. Phys., 16 (1970), pp. 310-328.

Glasser, M. L.

[1] Some definite integrals of the product of two Bessel functions of the second kind: (order zero), Math. Comp., 28 (1974), pp. 613-615.

Gronwall, T. H.

■fl] Uber die Gibbssche Erscheinung und die trigonometrischen Summen sin x + 12 sin 2x + • ■ ■ + (!/«) sin nx. Math. Ann., 72 (1912), pp. 228-243.

Grünbaum. F.

A property of Legendre polynomials, Proc. Nat. Acad. Sei., U.S.A., 67 (1970), pp. 959-960.

A new kind of inequality for Bessel functions, J. Math. Anal. Appl., 41 (1973), pp. 115-121.

Hardy, G. H.

Ramanujan, Cambridge University Press, Cambridge, 1940.

Further researches in the theory of divergent series and integrals. Trans. Camb. Phil. Soc., 21 (1908), pp. 1-48, reprinted in Collected Papers ofG. H. Hardy, vol. VI, 1974, pp. 214-262.

Hartman, P.

On differential equations and the function J* + K;, Amer. J. Math., 83 (1961), pp. 154-188.

On differential equations, Volterra equations and the function J* + Yj Ibid., 95 (1973) pp. 553-593.

Hartman, P. and G. S. Watson

[I] "Normal" distribution functions on spheres and the modified Bessel functions. Annals of Prob., 2(1974), pp. 593-607.

Hartman, P. and A. Wintner

[I] On nonconservative linear oscillators of low frequency, Amer. J. Math., 70 (1948), pp. 529-539.

Helgason, S.

[ I ] The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grossman manifolds. Acta Math., 113 (1965), pp. 153-180.

Henrici, P.

Addition theorems for general Legendre and Gegenbauer functions, J. Rational Mech. Anal. (now Indiana J. Math ), 4 (1955), pp. 983-1018.

My favorite proof of Mehler's integral, Amer. Math. Monthly, 78 (1971), pp. 183-185.

Hermite, C. and T. J. Stieltjes

[I] Correspondence d'Hermite et de Stieltjes, vol. 2, Gauthier-Villars, Paris, 1905, p. 43.

Hille, E.

[1] Note on some hypergeometric series of higher order, Proc. London Math. Soc., 4 (1929), pp. 50-54.

Hirschman, 1.1., Jr.

Variation diminishing Hankel transforms, J. Analyse Math., 8 (1960-61), pp. 307-336.

Extreme eigenvalues of Toeplitz forms associated with ultraspherical polynomials, J. Math. Mech. (now Indiana J. Math.), 13 (1964), pp. 249-282.

Eigenvalues of Toeplitz operators on SU(2), Duke Math. J., 41 (1974), pp. 51-82.

Hobson, E. W.

[1] The Theory of Spherical and Ellipsoidal Harmonics, Cambridge University Press, Cambridge, 1931.

hollô, â.

[1] A mechanikus quadraturdrôl, Thesis, Budapest, 1939, 23p.

Horton, R. L.

Expansions using orthogonal polynomials, Ph.D. thesis. University of Wisconsin, Madison, 1973.

Jacobi polynomials. IV, A family of variation diminishing kernels, SIAM J. Math. Anal., 6 (1975), pp. 544-550.

Hsü, H. Y.

[1] Certain integrals and infinite series involving ultraspherical polynomials and Bessel functions, Duke Math. J., 4 (1938), pp. 374-383.

Hua, L. K.

[I] Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, Trans. Math. Monographs 6, 1963, American Mathematical Society, Providence, R.I.

Huszàr, M.

[1] Symmetries of Wigner coefficients and Thomae-Whippie functions, Acta Phys. Acad. Sei. Hungar., 32 (1972), pp. 181-185.

Hylleraas, E.

[1] Linearization of products of Jacobi polynomials. Math. Scand., 10(1962), pp. 189-200.

Hyltén-Cavallius, C.

[I] A positive trigonometrical kernel, Tolfte Skand. Mat. Kongr. 1953 Lund (1954), pp. 90-94.

Igari, S. and Y. Uno

[I] Banach algebras related to the Jacobi polynomials. Tôhoku Math. J., 21 (1969), pp. 668-673.

iverson, k.

[I] The zeros of the partial sums of er, M.T.A.C. (now Math. Comp.), 7 (1953), pp. 165-168.

Jackson, D.

[1] Über eine trigonometrische Summe, Rend. Cire. Mat. Palermo, 32 (1911), pp. 257-262

Jacobi, C. G. J.

[I] Untersuchungen über die Differentialgleichung der hypergeometrischen Reihe, J. Reine Angew. Math., 56 (1859), pp. 149-165. Gesammelte Werke, Vol. 6, pp. 184-202.

Kaluza, T.

[1] Elementarer Beweis einer Vermutung von K. Friedrichs und H. Lewv, Math. Zeit., 37 (1933), pp. 689-697.

Karlin, S. and J. McGregor

The differential equations of birth-and-death processes, and the Stieltjes moment problem. Trans. Amer. Math. Soc., 85 (1957), pp. 489-546.

Classical diffusion processes and total positivity, J. Math. Anal. Appl., 1 (1960), pp. 163-183.

The Hahn polynomials, formulas and an application, Scripta Math., 26 (1961), pp. 33-46.

Karlin, S. and G. Szego

[I] On certain determinants whose elements are orthogonal polynomials, J. Analyse Math., 8 (1961), pp. 1-157.

Knuth, D.

[1] The Art of Computer Programming, Vol. I. Fundamental Algorithms, 2nd ed., Addison- Wesley, Reading, Mass., 1973.

Kogbetliantz, E.

[1] Recherches sur la sommabilité des séries ultrasphériques par la méthode des moyennes arith­métiques, J. Math. Pures Appl. (9), 3 (1924), pp. 107-187.

Koornwinder, T. H.

The addition formula for Jacobi polynomials. /, Summary of results, Indag. Math., 34 (1972), pp. 188-191.

The addition formula for Jacobi polynomials. II, The Laplace type integral representation and the product formula. Math. Centrum Amsterdam. Rep. TW 133 (1972).

The addition formula for Jacobi polynomials. Ill, Completion of the proof, Math. Centrum Amsterdam, Rep. TW 135 (1972).

The addition formula for Jacobi polynomials and spherical harmonics, SIAM J. Appl. Math., 25 (1973). pp. 236-246.

Jacobi polynomials. II, An analytic proof of the product formula, SI AM J. Math. Anal.. 5 ( 1974). pp. 125-137.

Orthogonal polynomials in two variables which are eigenfunctions of two algebraically indepen­dent partial differential operators. I, II, Indag. Math., 36 (1974). pp. 48-58; pp. 59-66.

Jacobi polynomials. III, An analytic proof of the addition formula, SIAM J. Math. Anal., 6 (1975), pp. 533-543.

Jacobi polynomials and their two-variable analogues. Thesis. University of Amsterdam. 1974.

A new proof of a Paley-Wiener type theorem for the Jacobi transform. Math. Centrum Amster­dam. Rep. TW 143(1974).

[ 10] The addition formula for Jacobi polynomials and the theory of orthogonal polynomials in two variables, a survey. Math. Centrum Amsterdam, Rep. TW 145 (1974).

koschmieder. l. and r. stroman

[I] Zwei Lösungen der Aufgabe 77. Jahr. Deutsch. Math. Verein., 43 (1933). pp. 64-66.

Koshliakov. N. S.

[1] On Sonine's polynomials. Mess. Math.. 55 (1926). pp. 152-160.

Kummer. E. E.

[I] Über die hypergeometrische Reihe, J. Reine Angew. Math., 15 (1836), pp. 39-83. 127-172.

Laplace. P.

[I] Théorie des attractions des sphéroides et de la figure des planètes, Mem. de l'Acad. Royale des Sciences de Paris (1782) (published in 1785). pp. 113-196; reprinted in Oeuvres de Laplace. 10(1894). pp. 339-419.

Lorch. L.

[I] Comparison of two formulations of Sonine's theorem and of their respective applications to Bessel functions, Studia Sei. Math. Hungar.. I (1966). pp. 141-145.

Lorch, L.. M. E. Muldoon and P. Szego

[I] Higher monotonicity properties of certain Sturm-Liouville functions, IV, Canad. J. Math., 24 (1972). pp. 349-368.

Lorentz. G. G. and K. Zeller

[I] Abschnittslimitierbarkeit und der Sat: von Hardy-Bohr, Arch. Math. (Basel). 15 (1964). pp. 208-213.

Luke, Y. L., W. Fair. G. Coombs and R. Moran

[1] On a constant in the theory of trigonometric series, Math. Comp., 19 (1965). pp. 501-502.

MacMahon. P. A.

[I] Combinatory Analysis, vol. I. Cambridge University Press. Cambridge. 1915.

Makai, E.

On a monotonie property of certain Sturm-Liouville functions. Acta Math. Acad. Sei. Hungar.. 3 (1952). pp. 165-171.

An integral inequality satisfied by Bessel functions. Ibid., 25 (1974). pp. 387-390.

Manocha. H. L.

[I] Some formulae involving AppeU's function Publ. Inst. Math. (Beograd) (N.S.), 9 (23), (1969), pp. 153-156.

Marx. A.

[I] Aufgaben 77. Jahr. Deutsch. Math. Verein.. 39 (1930). p. 1.

Mehler. F. G.

[I] Über eine mit den Kugelfunktionen und Cylinder funktionen verwandte Funktion und ihre Anwendung in der Theorie der Elektrizitätsverteilung, Math. Ann.. 18 (1881). pp. 161-194.

Mercer, A. McD.

On certain functional identities in ECanad. J. Math., 23 (1971), pp. 315-324.

Grunbaiim's inequality for Bessel functions and extensions of it, SIAM J. Math. Anal., to appear.

Miech. R. J.

Some p groups of maximal class. Trans. Amer. Math. Soc., 189 (1974). pp. 1-47.

Counting commutators. Ibid.. 189 (1974). pp. 49-61.

Miller, W.

Lie Theory and Special Functions, Academic Press, New York, 1968.

Special functions and the complex Euclidean group in 3-space, II, J. Math. Phys., 9 (1968), pp. 1175-1187.

Moses, J.

[1] Towards a general theory of special functions, Comm. A.C.M., 15 (1972), pp. 550-554. Müller. C.

[I] Spherical Harmonics, Lecture Notes in Mathematics, no. 17, Springer-Verlag, Berlin, 1966. Mullin, R. and G. C. Rota

[ 1 ] On the foundations of combinatorial theory, III: Theory of binomial enumeration. Graph Theory and its Applications. B. Harris, ed.. Academic Press, New York, 1970, pp. 167-213. Needham, J.

[1] Science and Civilization in China, vol. 3, Mathematics and the Sciences of the Heavens and the Earth, Cambridge University Press. New York. 1959. Nelson. E.

[I] The free Markofffield, J. Functional Anal.. 12 (1973). pp. 211-227. Neumann. F. E.

[1] Beiträge zur Theorie der Kugelfunctionen, Leipzig, 1878. von Neumann, J. and I. J. Schoenberg

[1] Fourier integrals and metric geometry, Trans. Amer. Math. Soc., 50 (1941). pp. 226-251. Newman. D. J. and T. J. Rivlin

[1] The zeros of the partial sums of the exponential function, i. Approximation Theory, 5 (1972), pp. 405-412. Nielson, N.

[I] Théorie des fonctions métasphériques, Paris. 1911. Novikoff. A.

[1] On a special system of orthogonal polynomials. Dissertation. Stanford University. 1954. avail­able from University Microfilms, Ann Arbor. Orihara. A.

[I] Hermitian polynomials and infinite-dimensional motion group, J. Math. Kyoto Univ., 6 (1966), pp. 1-12. Parrish, C.

[1] Multivariate umbral calculus, Ph.D. thesis. University of California at San Diego, La Jolla, 1974. Peetre, J.

[I] The Wey! transform and Laguerrepolynomials, Matematiche, 27 (1972), pp. 301-323. Pfaff, J. F.

Disquisitiones Analyticae, Helmstadii. 1797.

Observations analyticae ad L. Euleri Institutiones Calculi Integra/is, vol. IV, Supplem. II et IV, Historie de 1793, Nova acta academiae scientiarum Petropolitanae, Tom XI, 1797, pp. 38-57. (Note, the history section is paged separately from the scientific section of this journal.)


Über die Nullstellen gewisser ganzer Funktionen, Math. Zeit., 2 (1918), pp. 352-383.

Über die Konvergenz von Quadraturverfahren, Ibid., 37 (1933), pp. 264-286.

Remark on characteristic functions, Proc. First Berkeley Symp. on Stat, and Prob., University of California Press, Berkeley, 1949, pp. 63-78.

Pôlya, G. and I. J. Schoenberg

[1] Remarks on the de la Vallée Poussin means and convex conformai maps of the circle. Pacific J. Math., 8 (1958). pp. 295-334. Racah, G.

[1] Theory of complex spectra, II, Phys. Rev., 62 (1942), pp. 438-462.

Rainville, E. R.

[1] Special Functions, Macmillan. New York, 1960. Rankin, R. A.

[1] Functions whose powers have non-negative Taylor coefficients, Proc. London Math. Soc., I4A (1965), pp. 239-248. Regge, T.

[I] Symmetry properties of Oebsch-Gordan's coefficients, Nuovo Cimento (10). 10 (1958), pp. 544-545. Robertson, M. S.

The coefficients of univalent functions. Bull. Amer. Math. Soc.. 51 (1945). pp. 733-738.

Power series with multiply monotonie coefficients, Mich. Math. J., 16 (1969), pp. 27-31. Robin, L.

[I] Fonctions sphériques de Legendre et fonctions sphéroidales, vol. 3, Gauthier-Villars, Paris, 1959.

Rogosinski, W. and G. Szegö

[1] Über die Abschnitte von Potenzreihen, die in einem Kreise beschränkt bleiben, Math. Zeit.. 28 (1928), pp. 73-94. Rota, G.-C-, D. Kahaner and A. Odlyzko

[I] On the foundations of combinatorial theory, VII I, J. Math. Anal. Appl.. 42 (1973). pp. 684-760. Rudin, W.

[I] Fourier Analysis on Groups, Interscience, New York, 1962. Saft, E. and R. Varga

[I] Zero-free parabolic regions for sequences of polynomials, SIAM J. Math. Anal., to appear. Sapiro, R. L.

[I] Special functions related to representations of the group SU(n), of class I with respect to SV(n - 1 )(n 1 3). Izv. Vyssh. Uchebn. Zaved. Matematika (1968), no. 4 (71), pp. 97-107. (In Russian.) Sarmanov, I. O.

[1] A generalized symmetric gamma correlation, Dokl. Akad. Nauk SSSR, 179 (1968), pp. 1276— 1278; Soviet Math. Dokl., 9 (1968). pp. 547-550. Sarmanov, O. V. and Z. N. Bratoeva

[1] Probabilistic properties of bilinear expansions of Hermite polynomials. Theory Prob. Applica­tions, 12(1967), pp. 470-481. Schindler. S.

[I] Some transplantation theorems for the generalized Mehler transform and related asymptotic expansions. Trans. Amer. Math. Soc., 155 (1971), pp. 257-291. Schoenberg. I. J.

Metric spaces and completely monotonie functions, Ann. of Math.. (2), 39 (1938), pp. 811-841.

Positive definite functions on spheres, Duke Math. J., 9 (1942), pp. 96-108. Schweitzer. M.

[1] The partial sums of second order of the geometric series. Ibid.. 18 (1951), pp. 527-533. Seidel, W. and O. Szàsz

[1] On positive harmonic functions and ultraspherical polynomials, J. London Math. Soc., 26 (1951), pp. 36-41. Sonine, N. J.

[1] Recherches sur les fonctions cylindriques et le développement des fonctions continues en séries, Math. Ann., 16 (1880), pp. 1-80. Steinig, J.

The sign of Lommer s function, Trans. Amer. Math. Soc.. 163 (1972), pp. 123-129.

A criterion for the posit ivity ofsine polynomials, Proc. Amer. Math. Soc., 38 (1973), pp. 583-586. Stirling, J.

[1] Methodus differentialis; sive, Tractatus de summatione et interpolatione serierum infinitarum, London, 1730.

szegö, G.

Koeffizientenabschätzungen bei ebenen und räumlichen harmonischen Entwicklungen, Math. Ann., 96 (1927). pp. 601-632.

Zur Theorie der Legendreschen Polynome. Jahr. Deutsch. Math. Verein., 40 (1931), pp. 163-166.

Asymptotische Entwicklungen der Jacobischen Polynome, Sehr, der König. Gelehr. Gesell. Naturwiss. Kl.. 10 (1933), pp. 33-112.

Über gewisse Potenzreihen mit lauter positiven Koeffizienten, Math. Zeit.. 37 (1933). pp. 674-688.

Inequalities for the zeros of Legendre polynomials and related functions, Trans. Amer. Math. Soc., 39 (1936), pp. 1-17.

On some Hermitian forms associated wiih two given curves of the complex plane, Ibid., 40 (1936). pp. 450-461.

Power series with multiply monotonie sequences of coefficients, Duke Math. J., 8 (1941). pp. 559-564.

On the relative extrema of Legendre polynomials. Boll. Un. Mat. Ital., (3). 5 ( 1950). pp. 120-121.

Orthogonal Polynomials, Colloquium Publications, vol. 23, 3rd ed., American Mathematical Society, Providence, R.I., 1967.

Takàcs, L.

[I] On an identity of Shih-Chieh Chu, Acta Sei. Math. (Szeged), 34 (1973), pp. 383-391. Thomae, J.

[I] Über die Funktionen welche durch Reihenvon der Form dargestellt werden 1 + pp'p",\q'q" + •••, J. Reine Angew. Math., 87 (1879). pp. 26-73. Titchmarsh, E. C.

[I] Some integrals involving Hermitepolynomials, J. London Math. Soc., 23 (1948), pp. 15-16. TURAN, P.

On a trigonometrical sum. Ann. Soc. Polonaise Math.. 25 (1952), pp. 155-161.

On some problems in the theory of the mechanical quadrature, Mathematica (Cluj). (31). 8 (1966). pp. 181-192.

Tyan, S.-G.

[1] The structure of bivariate distribution functions and their relation to Markov processes, Ph.D. thesis, Princeton University, 1975. Tyan, S. and J. B. Thomas

[I] Characterization of a class of bivariate distribution functions, J. Multivariate Analysis. ( 1975). to appear. de la Vallée Poussin, C. J.

[1] Sur l'approximation des fonctions de variables réelles et de leurs dérivées par des polynomes et des suites limitées de Fourier, Bull, de l'Acad. Roy. de Belgique (Classe des Sciences), no. 3, 1908. Vandermonde, A.

[Il Mémoire sur des irrationnelles de différens ordres avec une application au cercle, Mem. Acad. Roy. Sei. Paris (1772), pp. 489-498. Vere-Jones. D.

[1] Finite bivariate distributions and semigroups of nonnegative matrices, Quart. J. Math., Oxford (2). 22 (1971). pp. 247-270. Vietoris, L.

[1] Über das Vorzeichen gewisser trigonometrischer Summen, Sitzungsber. Oest. Akad. Wiss., 167 (1958), pp. 125-135, and Anzeiger Oest. Akad. Wiss. (1959), pp. 192-193. Vilenkin, N. Ja.

Some relations for Gegenbauer functions, Uspekhi Matern. Nauk (N.S.), 13 (1958), no. 3 (81), pp. 167-172. (In Russian.)

Special Functions and the Theory of Group Representations, Translations of Math. Mono­graphs, vol. 22, American Mathematical Society, Providence, 1968.

Wall, H. S.

[1] A class offunctions bounded in the unit circle, Duke Math. J., 7 (1940), pp. 146-153.Watson. G. N.

Another note on Laguerrepolynomials, J. London Math. Soc.. 14 (1939), pp. 19-22.

A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge University Press, Cambridge, 1944.

A reduction formula, Proc. Glasgow Math. Assoc., 2 (1954), pp. 57-61. Weinberger, H.

[I] A maximum property of Cauchy s problem, Ann. of Math. (2), 64(1956), pp. 505-513. Whipple, F. J. W.

A group of generalized hypergeometric series: relations between 120 allied series of the type F[';bf], Proc. London Math. Soc.'(2), 23 (1924), pp. 104-114.

Well-poised series, generalized hypergeometric series having parameters in pairs, each pair having the same sum. Ibid., 24 (1925), pp. 247-263.

H ell-poised series and other generalized hypergeometric series, Ibid., 25 ( 1926), pp. 525-544. Whittaker, E. T. and G. N. Watson

[1] A Course of Modern Analysis, 4th ed., Cambridge University Press, Cambridge, 1952. Wilken, D. R.

[1] The integral means of close-to-convex functions, Mich. Math. J., 19 (1972), pp. 377-379. Wilson, M. W.

On the Hahn polynomials, SIAM J. Math. Anal., 1 (1970), pp. 131-139.

Nonnegative expansions of polynomials, Proc. Amer. Math. Soc.. 24(1970), pp. 100-102.

On a new discrete analogue of the Legendre polynomials, SIAM J. Math. Anal., 3 (1972), pp. 157-169.

Wimp, J.

[1] On the zeros of a confluent hypergeometric function, Proc. Amer. Math. Soc., 16 (1965), pp. 281-283. Young, W. H.

On a certain series of Fourier, Proc. London Math. Soc. (2), 11 (1912), pp. 357-366.

On the Fourier series of bounded functions, Ibid., 12 (1913), pp. 41-70. Zaremba, S. K.

[1] Some properties of polynomials orthogonal over the set <1,2, • • • , N), Mathematics Research Center, Tech. Rep. 1342, University of Wisconsin, Madison. Zernike, F. and H. C. Brinkman

[1] Hypersphärische Funktionen und die in sphärischen Bereichen orthogonalen Polynome, Nederl. Akad. Wetensch. Proc.. 38 (1935). pp. 161-J70.