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Unified (p, q)-Bernoulli-Hermite polynomials

Pathan M. A.

Fasciculi Mathematici

2018

Nr 61

125--141

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), respec- tively. Some properties, generating functions and Laplace hy- pergeometric 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.

Multivalent Harmonic Functions defined by m-tuple Integral operators

Sharma P.

Commentationes Mathematicae

2010

Vol. 50, [Z] 1

87-101

Asymptotic formulas for unified elliptic-type integrals

Saxena R. K., Pathan M. A.

Demonstratio Mathematica

2003

Vol. 36, nr 3

579--589

The object of this article is to present a unification and generalisation of certain families of elliptic-type integrals which were studied in a number of earlier works on the subject due to their importance for possible applications in certain problems arising in radiation physics and nuclear technology. The results obtained are of general character and include the investigations carried out by several authors including Srivastava and Siddiqi, Kalla and Tuan, Al-Zamel et al and Saxena et al.