An Integral Representation and Some Summation Formulas for the Hahn Polynomials

Next article An Integral Representation and Some Summation Formulas for the Hahn PolynomialsP. A. LeeP. A. Leehttps://doi.org/10.1137/0119025PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] W. A. Al-Salam, Operational representations for the Laguerre and other polynomials, Duke Math. J., 31 (1964), 127–142 10.1215/S0012-7094-64-03113-8 MR0159053 (28:2271) 0124.03402 CrossrefISIGoogle Scholar[2] John J. Bartko, Mathematical Notes: Some Summation Theorems on the Hahn Polynomials, Amer. Math. Monthly, 70 (1963), 978–981 MR1532371 0122.31401 CrossrefISIGoogle Scholar[3] John J. Bartko and , Geoffrey A. Watterson, Inference on a genetic model of the Markov chain type, Biometrika, 50 (1963), 251–264 MR0163389 (29:692) 0118.34602 CrossrefISIGoogle Scholar[4] L. Carlitz, On the product of two Laguerre polynomials, J. London Math. Soc., 36 (1961), 399–402 MR0140725 (25:4139) 0107.05602 CrossrefGoogle Scholar[5] Artur Erdélyi, Über einige bestimmte Integrale, in denen die Whittakerschen M k,m-Funktionen auftreten, Math. Z., 40 (1936), 693–702 MR1545593 0013.06405 CrossrefGoogle Scholar[6] Arthur Erdélyi, , Wilhelm Magnus, , Fritz Oberhettinger and , Francesco G. Tricomi, Higher transcendental functions. Vol. I, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953xxvi+302 MR0058756 (15,419i) 0051.30303 Google Scholar[7] Arthur Erdélyi, , Wilhelm Magnus, , Fritz Oberhettinger and , Francesco G. Tricomi, Higher transcendental functions. Vol. II, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953xvii+396 MR0058756 (15,419i) 0052.29502 Google Scholar[8] A. Erdélyi, , W. Magnus, , F. Oberhettinger and , F. G. Tricomi, Tables of integral transforms. Vol. I, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1954xx+391 MR0061695 (15,868a) 0055.36401 Google Scholar[9] Wolfgang Hahn, Über Orthogonalpolynome, die q-Differenzengleichungen genügen, Math. Nachr., 2 (1949), 4–34 MR0030647 (11,29b) 0031.39001 CrossrefGoogle Scholar[10] Samuel Karlin and , James L. McGregor, The Hahn polynomials, formulas and an application, Scripta Math., 26 (1961), 33–46 MR0138806 (25:2249) 0104.29103 Google Scholar[11] Samuel Karlin and , James McGregor, On a genetics model of Moran, Proc. Cambridge Philos. Soc., 58 (1962), 299–311 MR0138144 (25:1591) 0218.60073 CrossrefISIGoogle Scholar[12] S Karlin and , J McGregor, J. Curland, On some stochastic models in geneticsStochastic Models in Medicine and Biology, University of Wisconsin Press, Madison, 1964, 245–279 0146.15801 Google Scholar[13] P. A. Lee, On integrals involving parabolic cylinder functions, J. Math. and Phys., 46 (1967), 215–219 MR0212233 (35:3107) 0177.09503 CrossrefISIGoogle Scholar[14] Peter Lesky, Die Übersetzung der klassischen orthogonalen Polynome in die Differenzenrechnung, Monatsh. Math., 65 (1961), 1–26 10.1007/BF01322656 MR0124639 (23:A1951) 0097.05501 CrossrefGoogle Scholar[15] Peter Lesky, Orthogonale Polynomsysteme als Lösungen Sturm-Liouvillescher Differenzengleichungen, Monatsh. Math., 66 (1962), 203–214 10.1007/BF01299044 MR0139861 (25:3288) 0105.05302 CrossrefGoogle Scholar[16] R. J. Levit, The zeros of the Hahn polynomials, SIAM Rev., 9 (1967), 191–203 10.1137/1009032 MR0213627 (35:4485) 0154.06601 LinkISIGoogle Scholar[17] Karl Mayr, Integraleigenschaften der Hermiteschen und Laguerreschen Polynome, Math. Z., 39 (1935), 597–604 10.1007/BF01201375 MR1545519 0010.30103 CrossrefGoogle Scholar[18] Maria Weber and , A. Erdélyi, On the finite difference analogue of Rodrigues' formula, Amer. Math. Monthly, 59 (1952), 163–168 MR0054094 (14,871d) 0046.29902 CrossrefGoogle Scholar Next article FiguresRelatedReferencesCited ByDetails Modified Clebsch-Gordan-type expansions for products of discrete hypergeometric polynomialsJournal of Computational and Applied Mathematics, Vol. 89, No. 1 | 1 Mar 1998 Cross Ref Multivariable biorthogonal Hahn polynomialsJournal of Mathematical Physics, Vol. 30, No. 3 | 1 Mar 1989 Cross Ref Projection formulas for orthogonal polynomials of a discrete variableJournal of Mathematical Analysis and Applications, Vol. 45, No. 1 | 1 Jan 1974 Cross Ref Volume 19, Issue 2| 1970SIAM Journal on Applied Mathematics266-485 History Submitted:13 August 1968Published online:17 February 2012 InformationCopyright © 1970 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0119025Article page range:pp. 266-272ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics