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A new class of generating functions for Chebyshev polynomials. (English) Zbl 1268.33008

Summary: The main aim of this paper is to define and study a new family of generating functions and identities concerning the Chebyshev polynomials. The hypergeometric representations of these polynomials are given. It is shown that the proposed method allows the derivation of an expansions in a series of Chebyshev polynomials.

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
35A22 Transform methods (e.g., integral transforms) applied to PDEs
45P05 Integral operators
47G10 Integral operators
65R10 Numerical methods for integral transforms
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References:

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