Construction of some new families of Apostol-type numbers and polynomials via Dirichlet character and p-adic q-integrals
By Yilmaz Simsek. 2018
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In this paper, by applying the p -adic q -integrals to a family of continuous differentiable functions on the ring of p -adic integers, we construct new generating functions for generalized Apostol-type numbers and polynomials attached to the Dirichlet character of a finite abelian group. By using these generating functions with their functional equations, we derive various new identities and relations for these numbers and polynomials. These results are generalizations of known identities and relations including some well-known families of special numbers and polynomials such as the generalized Apostol-type Bernoulli, the Apostol-type Euler, the Frobenius–Euler numbers and polynomials, the Stirling numbers, and other families of numbers and polynomials. Moreover, by the help of these generating functions, we also construct other new families of numbers and polynomials with their generating functions. By using these functions, we investigate some fundamental properties of these numbers and polynomials. Finally, we also give explicit formulas for computing the Apostol–Bernoulli and Apostol–Euler numbers.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e0198562864cd1beb957625d62ec85baa89ebedd
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Mathematical Physics
Citations in the corpus
- Explicit formulas for p-adic integrals: approach to p-adic distributions and some families of special numbers and polynomials. (2019, background): “[108], [111]) so that the numbers Yn (λ) are defined by the author in (cf.”