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Some identities involving Gegenbauer polynomials. (English) Zbl 1377.33008

Summary: In this paper, we derive some interesting identities involving Gegenbauer polynomials arising from the orthogonality of Gegenbauer polynomials for the inner product space \(\mathbb P_n\) with respect to the weighted inner product \(\langle p_1,p_2\rangle =\int^1_{-1}p_1(x)p_2(x)(1-x^2)^{\lambda-\frac{1}{2}}dx\).

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
11B68 Bernoulli and Euler numbers and polynomials
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References:

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