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A combinatorial formula of Leibniz type
with application to Gegenbauer's polynomials


Authors: Katsunori Iwasaki and Hiroyuki Kawamuko
Journal: Proc. Amer. Math. Soc. 127 (1999), 29-33
MSC (1991): Primary 05A19, 33C45, 42C05
DOI: https://doi.org/10.1090/S0002-9939-99-04677-8
MathSciNet review: 1476139
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Abstract | References | Similar Articles | Additional Information

Abstract: We establish a combinatorial formula of Leibniz type, which is an identity for a certain differential polynomial. The formula leads to new quadratic relations between Gegenbauer's orthogonal polynomials.


References [Enhancements On Off] (What's this?)

  • 1. A. Erdélyi, et al., Higher transcendental functions, Vol. 1, MacGraw Hill, New York, 1953. MR 84m:33001a
  • 2. O. Hölder, Uber die Eingenschaft der Gammafunction keiner algebraischen Differentialgleichung zu genügen, Math. Ann. 28 (1887), 1-13.
  • 3. H. Kawamuko, Studies on the fourth Painlevé equation in several variables, Ph. D. dissertation, The University of Tokyo, 1997.

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Additional Information

Katsunori Iwasaki
Affiliation: Department of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581 Japan
Email: iwasaki@math.kyushu-u.ac.jp

Hiroyuki Kawamuko
Affiliation: Department of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153 Japan
Address at time of publication: Department of Mathematics, Mie University, 1515 Kamihama, Tsu 514-8507, Japan
Email: kawam@poisson.ms.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-99-04677-8
Keywords: Combinatorial formula of Leibniz type, Gegenbauer's polynomials, transcendency of the Gamma function
Received by editor(s): May 2, 1997
Communicated by: Hal L. Smith
Article copyright: © Copyright 1999 American Mathematical Society

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