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A combinatorial formula of Leibniz type with application to Gegenbauer's polynomials |
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| Authors: | Katsunori Iwasaki Hiroyuki Kawamuko |
| Affiliation: | Department of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581 Japan ; Department of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153 Japan |
| 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. |
| Keywords: | Combinatorial formula of Leibniz type Gegenbauer's polynomials transcendency of the Gamma function |
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