Open AccessCombinatorial 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.