Combinatorial identities for Appell polynomials | Zendy

Emanuele Munarini | Zendy

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Combinatorial identities for Appell polynomials

Author(s) -

Emanuele Munarini

Publication year - 2018

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm161001004m

Subject(s) - mathematics , orthogonal polynomials , laguerre polynomials , classical orthogonal polynomials , wilson polynomials , difference polynomials , legendre polynomials , discrete orthogonal polynomials , appell series , hermite polynomials , pure mathematics , bernoulli polynomials , algebra over a field , hypergeometric function , generalized hypergeometric function , mathematical analysis , hypergeometric function of a matrix argument

Using the techniques of the modern umbral calculus, we derive several combinatorial identities involving s-Appell polynomials. In particular, we obtain identities for classical polynomials, such as the Hermite, Laguerre, Bernoulli, Euler, N?rlund, hypergeometric Bernoulli, and Legendre polynomials. Moreover, we obtain a generalization of Carlitz's identity for Bernoulli numbers and polynomials to arbitrary symmetric s-Appell polynomials.

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