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On finite sums of Laguerre polynomials. (English) Zbl 1214.33004

The author considers finite sums of Laguerre polynomials and writes them in terms of Laguerre polynomials themselves or as confluent or other hypergeometric functions. He gives alternative approaches using contour integration and other integral representations. He also finds a Kummer-like transformation for a particular generalized hypergeometric function \(_{2}F_{2}\) in terms of Laguerre polynomials.

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)
33C20 Generalized hypergeometric series, \({}_pF_q\)
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References:

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