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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
MathSciNet review:
1476139
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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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