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Laguerre-based Hermite-Bernoulli polynomials associated with bilateral series. (English) Zbl 1431.33012

Summary: In the paper, we define Laguerre-based Hermite-Bernoulli polynomial with its generating function, and investigate certain properties. From this generating function, we derive summation formulas and related bilateral series associated with the newly introduced generating function. Some of whose special cases are also presented. Relevant connections of some results presented here with those involving simpler known partly unilateral and partly bilateral representations are also obtained.

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
11B68 Bernoulli and Euler numbers and polynomials
33C05 Classical hypergeometric functions, \({}_2F_1\)
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References:

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