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

Author(s): Katsunori Iwasaki; Hiroyuki Kawamuko
Journal: Proc. Amer. Math. Soc. 127 (1999), 29-33.
MSC (1991): Primary 05A19, 33C45, 42C05
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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:

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: 10.1090/S0002-9939-99-04677-8
PII: S 0002-9939(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
Copyright of article: Copyright 1999, American Mathematical Society


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