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BILINEAR AND BILATERAL GENERATING FUNCTIONS OF HEAT TYPE POLYNOMIALS SUGGESTED BY JACOBI POLYNOMIALS
Khan, Mumtaz Ahmad,Khan, Abdul Hakim,Singh, Manoj Korean Mathematical Society 2011 대한수학회논문집 Vol.26 No.4
The present paper deals with generalization of several families of bilinear and bilateral generating functions for the heat type polynomials suggested by Jacobi polynomials with different argument.
Khan, Nabiullah,Nadeem, Raghib,Usman, Talha,Khan, Abdul Hakim The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.1
In the last decades, various integral formulas associated with Bessel functions of different kinds as well as Bessel functions themselves, have been studied and a noteworthy amount of work can be found in the literature. Following up, we present two definite integral formulas involving the product of generalized Bessel function associated with orthogonal polynomials. Also, some intriguing special cases of our main results have been discussed.
ON ESTIMATION OF UNIFORM CONVERGENCE OF ANALYTIC FUNCTIONS BY (p, q)-BERNSTEIN OPERATORS
Mursaleen, M.,Khan, Faisal,Saif, Mohd,Khan, Abdul Hakim The Kangwon-Kyungki Mathematical Society 2019 한국수학논문집 Vol.27 No.2
In this paper we study the approximation properties of a continuous function by the sequence of (p, q)-Bernstein operators for q > p > 1. We obtain bounds of (p, q)-Bernstein operators. Further we prove that if a continuous function admits an analytic continuation into the disk $\{z:{\mid}z{\mid}{\leq}{\rho}\}$, then $B^n_{p,q}(g;z){\rightarrow}g(z)(n{\rightarrow}{\infty})$ uniformly on any compact set in the given disk $\{z:{\mid}z{\mid}{\leq}{\rho}\}$, ${\rho}>0$.
A STUDY OF NEW CLASS OF INTEGRALS ASSOCIATED WITH GENERALIZED STRUVE FUNCTION AND POLYNOMIALS
Haq, Sirazul,Khan, Abdul Hakim,Nisar, Kottakkaran Sooppy Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.1
The main aim of this paper is to establish a new class of integrals involving the generalized Galu$Galu{\grave{e}}$-type Struve function with the different type of polynomials such as Jacobi, Legendre, and Hermite. Also, we derive the integral formula involving Legendre, Wright generalized Bessel and generalized Hypergeometric functions. The results obtained here are general in nature and can deduce many known and new integral formulas involving the various type of polynomials.
GENERALIZATION OF MULTI-VARIABLE MODIFIED HERMITE MATRIX POLYNOMIALS AND ITS APPLICATIONS
Singh, Virender,Khan, Mumtaz Ahmad,Khan, Abdul Hakim The Honam Mathematical Society 2020 호남수학학술지 Vol.42 No.2
In this paper, we get acquainted to a new generalization of the modified Hermite matrix polynomials. An explicit representation and expansion of the Matrix exponential in a series of these matrix polynomials is obtained. Some important properties of Modified Hermite Matrix polynomials such as generating functions, recurrence relations which allow us a mathematical operations. Also we drive expansion formulae and some operational representations.
Talha Usman,Nabiullah Khan,Raghib Nadeem,Abdul Hakim Khan 호남수학회 2019 호남수학학술지 Vol.41 No.1
In the last decades, various integral formulas associated with Bessel functions of different kinds as well as Bessel functions themselves, have been studied and a noteworthy amount of work can be found in the literature. Following up, we present two definite integral formulas involving the product of generalized Bessel function associated with orthogonal polynomials. Also, some intriguing special cases of our main results have been discussed.
ON SOME GENERATING FUNCTIONS OF GENERALIZED BATEMAN'S AND PASTERNAK'S POLYNOMIALS OF TWO VARIABLES
Abbas, Sayed Mohammad,Khan, Mumtaz Ahmad,Khan, Abdul Hakim Korean Mathematical Society 2013 대한수학회논문집 Vol.28 No.1
The aim of the present paper is to study some generating functions of generalized Bateman's and Pasternak's polynomials of two variables.