Unified (p, q)-Bernoulli-Hermite polynomials
2018
scientific article
english
- Bernoulli polynomials and Bernoulli numbers
- generating functions
- Gauss hypergeometric function
- Hurwitz zeta function and Euler’s polynomials
EN The Concepts of p-Bernoulli numbers Bn, p and p-Bernoulli polynomials Bn, p (x) are generalized to (p,q)-Bernoulli numbers Bn, p, q and (p,q)-Bernoulli polynomials Bn, p, q (x), respectively. Some properties, generating functions and Laplace hypergeometric integral representations of (p, q)-Bernoulli numbers Bn, p, q and (p, q)-Bernoulli polynomials Bn, p, q (x), are established. Unified (p, q)-Bernoulli-Hermite polynomials are defined by a generating function which aid in proving the generalizations of the results of Khan et al [8], Kargin and Rahmani [7], Dattoli [4] and Pathan [9]. Some explicit summation formulas and some relationships between Appell’s function F1, Gauss hypergeomtric function, Hurwitz zeta function and Euler’s polynomials are also given.
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CC BY-NC-ND (attribution - noncommercial - no derivatives)
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