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On the multidimensional zeta functions associated with theta functions, and the multidimensional Appell polynomials
Author(s) -
Bayad Abdelmejid,
Hajli Mounir
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6075
Subject(s) - mathematics , generalization , pure mathematics , arithmetic zeta function , difference polynomials , orthogonal polynomials , algebra over a field , appell series , riemann zeta function , mathematical analysis , hypergeometric function , generalized hypergeometric function , hypergeometric function of a matrix argument
We define and study the multidimensional Appell polynomials associated with theta functions. For the trivial theta functions, we obtain the various well‐known Appell polynomials. Many other interesting examples are given. To push our study, by Mellin transform, we introduce and investigate the multidimensional zeta functions associated with thetas functions and prove that the multidimensional Appell polynomials are special values at the nonpositive integers of these zeta functions. Using zeta functions techniques, among others, we prove an induction formula for multidimensional Appell polynomials. The last part of this paper is devoted to spectral zeta functions and its generalization associated with Laplacians on compact Riemannian manifolds. From this generalization, we construct new Appell polynomials associated with Riemannan manifolds of finite dimensions.