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Adell, José A.; Lekuona, Alberto

Closed form expressions for Appell polynomials. (English) Zbl 1459.11055

Ramanujan J. 49, No. 3, 567-583 (2019).
Summary: We show that any Appell sequence can be written in closed form as a forward difference transformation of the identity. Such transformations are actually multipliers in the abelian group of the Appell polynomials endowed with the operation of binomial convolution. As a consequence, we obtain explicit expressions for higher order convolution identities referring to various kinds of Appell polynomials in terms of the Stirling numbers. Applications of the preceding results to generalized Bernoulli and Apostol-Euler polynomials of real order are discussed in detail.

Cited in 5 Documents

MSC:

11B68 Bernoulli and Euler numbers and polynomials
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
60E05 Probability distributions: general theory

Keywords:

Appell polynomials; binomial convolution; forward difference transformation; higher order convolution identities; generalized Bernoulli polynomials; generalized Apostol-Euler polynomials
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References:

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