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[8] L. Carlitz, Some polynomials related to the ultraspherical polynomials, Portugaliae Math. 20 (1961), 127–136. [9] A. Erdelyi, Higher Transcendental Functions, vols. 1 and 2, McGraw Hill, New York, 1953. [10] G. Gasper, Positive integrals of Bessel functions, SIAM J. Math. Anal. 6 (1975), 868–881. [11] G. Gasper, Positivity and special functions, in Theory and Applications of Special Functions, R. Askey, ed., Academic Press, New York (1975), 375–433. [12] G. Gasper, Positive sums of the classical orthogonal polynomials, SIAM J. Math. Anal. 8 (1977), 423–447. [13] G. Gasper, A short proof of an inequality used by de Branges in his proof of the Bieberbach, Robertson and Milin conjectures, Complex Variables: Theory Appl. 7 (1986), 45–50. [14] G. Gasper, q-Extensions of Clausen’s formula and of the inequalities used by de Branges in his proof of the Bieberbach, Robertson, and Milin conjectures, SIAM J. Math. Anal. 20 (1989), 1019–1034. [15] G. Gasper, Using symbolic computer algebraic systems to derive formulas involving orthogonal polynomials and other special functions, in Orthogonal Polynomials: Theory and Practice, ed. by P. Nevai, Kluwer Academic Publishers, Boston, 1989, 163–179. [16] G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, 1990. [17] E. Hille, Note on some hypergeometric series of higher order, J. London Math. Soc. 4 (1929), 50–54. [18] J.L.W.V. Jensen, Recherches sur la théorie des équations, Acta Math. 36 (1913), 181–195. [19] G. Pólya, Über die algebraisch-funktionentheoretischen Untersuchungen von J. L. W. V. Jensen, Kgl. Danske Videnskabernes Selskab. Math.-Fys. Medd. 7 (17) (1927), pp. 3–33; reprinted in his Collected Papers, Vol. II, pp. 278–308. [20] G. Szegő, Orthogonal Polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ. 23, Providence, R.I. 1975. [21] E.C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd edition (Revised by D.R. Heath-Brown), Oxford Univ. Press, Oxford and New York, 1986. [22] R.S. Varga, Scientific Computation on Mathematical Problems and Conjectures, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1990. [23] G.N. Watson, Theory of Bessel Functions, Cambridge Univ. Press, Cambridge and New York, 1944. 16
George Gasper Department of Mathematics Northwestern University Evanston, IL 60208 E-Mail: g-gasper@nwu.edu 17
Page 1 and 2: arXiv:math.CA/9307210 v1 9 Jul 1993
Page 3 and 4: is a nonnegative even convex functi
Page 5 and 6: 3 Bessel functions and 0 F 1 (c; z)
Page 7 and 8: and (3.12) ∂ 2 ∂y 2 |J α(z)| 2
Page 9 and 10: and (3.22) ∂ 2 ∂y 2 |c(c + 1) 0
Page 11 and 12: which are consequences of (4.6). No
Page 13 and 14: 5 Jacobi polynomials When α > −1
Page 15: for which the Jacobi polynomials ha

G. Gasper Using sums of squares to prove that ... - Fuchs-braun.com

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