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1

Unified (p, q)-Bernoulli-Hermite polynomials

Pathan M. A.

Fasciculi Mathematici

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2018

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Nr 61

125--141

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), 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.

2

Some new classes of generalized Hermite-Based Apostol-Euler and Apostol-Genocchi polynomials

Pathan M. A., Khan W. A.

Fasciculi Mathematici

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2015

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Nr 55

153--170

EN

In this paper, we introduce a new class of generalized Apostol-Hermite-Euler polynomials and Apostol-Hermi-te-Genocchi polynomials and derive some implicit summation formulae by applying the generating functions. These results extend some known summations and identities of generalized Hermite-Euler polynomials studied by Dattoli et al, Kurt and Pathan.

3

Laplace transforms of the logarithmic functions and their applications

Pathan M. A., Daman O.A.

Demonstratio Mathematica

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2013

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Vol. 46, nr 3

533--542

EN

This paper deals with theorems and formulas using the technique of Laplace and Steiltjes transforms expressed in terms of interesting alternative logarithmic and related integral representations. The advantage of the proposed technique is illustrated by logarithms of integrals of importance in certain physical and statistical problems.

4

Asymptotic formulas for unified elliptic-type integrals

Saxena R. K., Pathan M. A.

Demonstratio Mathematica

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2003

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Vol. 36, nr 3

579--589

EN

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.