Nabiullah Khan

A New Class of Laguerre-based Generalized Apostol Polynomials

Abstract In this paper, we introduce a unified family of Laguerre-based Apostol Bernoulli, Euler and Genocchi polynomials and derive some implicit summation formulae and general symmetry identities arising from different analytical means and applying generating functions. The result extend some known summations and identities of generalized Bernoulli, Euler and Genocchi numbers and polynomials.

Some bilateral generating relations involving Gegenbauer polynomials

In this paper, we obtain three interesting bilateral generating functions for Gegenbauer polynomials C n b (x) associated with hypergeometric polynomials 2 F 1, 1 F 2 and 3 F 2. Our results are obtained with the help of series rearrangement technique.

Certain unified polynomials

ABSTRACT We aim to introduce certain unified polynomials which can be specialized to yield a number of known polynomials and numbers, for example, Pell polynomials and numbers, Fibonacci polynomials and numbers, and -Fibonacci polynomials. Then we investigate the unified polynomials to present certain interesting and potentially useful properties such as explicit expressions, some recurrence relations, a differential equation, and several generating functions. Further, among a number of polynomials and numbers which can be specialized from the unified polynomials, we choose the Pell polynomials to record their corresponding properties.

A NOTE ON GENERALIZED EXTENDED WHITTAKER FUNCTION

In the present paper, we define the generalized extended Whittaker function in terms of generalized extended confluent hypergeometric function of the first kind. We also study its integral representation, some integral transforms and its derivative.

New class of generating functions associated with generalized hypergeometric polynomials

In this paper authors prove a general theorem on generating relations for a certain sequence of functions. Many formulas involving the families of generating functions for generalized hypergeometric polynomials are shown here to be special cases of a general class of generating functions involving generalized hypergeometric polynomials and multiple hypergeometric series of several variables. It is then shown how the main result can be applied to derive a large number of generating functions involving hypergeometric functions of Kampe de Feriet, Srivastava, Srivastava–Daoust, Chaundy, Fasenmyer, Cohen, Pasternack, Khandekar, Rainville and other multiple Gaussian hypergeometric polynomials scattered in the literature of special functions.