A Set of Hypergeometric Orthogonal Polynomials

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Previous article Next article A Set of Hypergeometric Orthogonal PolynomialsRichard Askey and James WilsonRichard Askey and James Wilsonhttps://doi.org/10.1137/0513043PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractPolynomials orthogonal with respect to $| {\Gamma (\alpha + ix)\Gamma (\gamma + ix)} |^2 $ on $( - \infty ,\infty )$ are found.[1] Richard Askey and , James Wilson, A set of orthogonal polynomials that generalize the Racah coefficients or $6-j$ symbols, SIAM J. Math. Anal., 10 (1979), 1008–1016 10.1137/0510092 80k:33012 0437.33014 LinkISIGoogle Scholar[2] H. Bateman, Functions orthogonal in the Hermitian sense, a new application of basic numbers, Proc. National Acad. Sci., 20 (1934), 63–66 0008.25801 CrossrefGoogle Scholar[3] L. Carlitz, Bernoulli and Euler numbers and orthogonal polynomials, Duke Math. J, 26 (1959), 1–15 21:2761 0085.28702 CrossrefISIGoogle Scholar[4] A. Erdélyi, Higher transcendental functions. Vol. I, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953xxvi+302 15,419i 0051.30303 Google Scholar[5] G. Freud, Orthogonal Polynomials, Pergamon Press, Oxford, 1971 Google Scholar[6] E. M. Nikishin, O. Lehto, The Padé approximants, Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Vol. 2, Acad. Sci. Fennica, Helsinki, 1980, 623–630 81d:30070 0441.30007 Google Scholar[7] M. H. Stone, Linear Transformations in Hilbert Space and Their Applications to Analysis, AMS Colloquium Publications, XV, American Mathematical Society, Providence, R.I., 1932 0005.40003 CrossrefGoogle Scholar[8] Jacques Touchard, Nombres exponentiels et nombres de Bernoulli, Canad. J. Math., 8 (1956), 305–320 18,16f 0071.06105 CrossrefGoogle Scholar[9] James Wilson, Some hypergeometric orthogonal polynomials, SIAM J. Math. 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