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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.
A NOTE ON GENERATING FUNCTIONS OF q-GOTTLIEB POLYNOMIALS
Khan, Mumtaz Ahmad,Asif, Mohammad Korean Mathematical Society 2012 대한수학회논문집 Vol.27 No.1
The present paper envisages the q-analogue of the Gottlieb polynomials.
Khan, Subuhi,Khan, Mumtaz Ahmad,Khan, Rehana Korean Mathematical Society 2009 대한수학회지 Vol.46 No.6
This paper is an attempt to stress the usefulness of the multivariable special functions. In this paper, we derive generating relations involving 3-variable 2-parameter Tricomi functions by using Lie-algebraic techniques. Further we derive certain new and known generating relations involving other forms of Tricomi and Bessel functions as applications.
Subuhi Khan,Mumtaz Ahmad Khan,Rehana Khan 대한수학회 2009 대한수학회지 Vol.46 No.6
This paper is an attempt to stress the usefulness of the multi-variable special functions. In this paper, we derive generating relations involving 3-variable 2-parameter Tricomi functions by using Lie-algebraic techniques. Further we derive certain new and known generating relations involving other forms of Tricomi and Bessel functions as applications.
EULER TYPE INTEGRAL INVOLVING GENERALIZED MITTAG-LEFFLER FUNCTION
Ahmed, Shakeel,Khan, Mumtaz Ahmad Korean Mathematical Society 2014 대한수학회논문집 Vol.29 No.3
In this paper, we obtain some theorems on certain Euler type integrals involving generalized Mittag-Leffler function. Further, we deduce some special cases involving Wiman function, Prabhakar function and exponential and binomial functions.
On some new type of generating functions of generalized Poisson-Charlier polynomials
Shakeel Ahmed,Mumtaz Ahmad Khan 대한수학회 2022 대한수학회논문집 Vol.37 No.1
The present paper concerns with a study of certain generating functions and summation formulas of generalized Poisson-Charlier polynomials. Some special cases are also discussed.
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.
ON SOME FORMULAS FOR THE GENERALIZED APPELL TYPE FUNCTIONS
Agarwal, Praveen,Jain, Shilpi,Khan, Mumtaz Ahmad,Nisar, Kottakkaran Sooppy Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.4
A remarkably large number of special functions (such as the Gamma and Beta functions, the Gauss hypergeometric function, and so on) have been investigated by many authors. Motivated the works of both works of both Burchnall and Chaundy and Chaundy and very recently, Brychkov and Saad gave interesting generalizations of Appell type functions. In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present some new differential formulas for the generalized Appell's type functions ${\kappa}_i$, $i=1,2,{\ldots},18$ by considering the product of two $_4F_3$ functions.
Anam Naseer,Muhammad Mumtaz,Muhammad Raffi,Izhar Ahmad,Sabih D. Khan,Rana I. Shakoor,Shaista Shahzada 대한금속·재료학회 2019 ELECTRONIC MATERIALS LETTERS Vol.15 No.2
With the recent developments in the millimeter and sub-millimeter wave instruments and devices, there is a need to developelectromagnetic (EM) wave absorbing materials in these frequency bands for applications like electromagnetic interferencecontrol, electromagnetic compatibility, etc. In this work, carbon nanofi bers (CNF) were uniformly dispersed in a blend ofpoly(methyl methacrylate), polyvinylidene fl uoride and cyanoacrylate for air spray coating a fi lm on the cellulosic substrates. The samples were characterized for evaluation of their structure, morphology, electrical and EM absorption properties in0.15–1.2 THz range by X-ray diff raction, fi eld emission electron microscopy, I–V measurements and terahertz time domainspectroscopy. These coatings can conveniently be applied to the material surfaces by conventional air spray painting method,which makes this technique cost-eff ective as well as easy to deploy in various applications. The electrical conductivityenhancement in the samples has been attributed to the formation of conducting network by uniform distribution of CNFs inthe insulating polymer matrix. As a result, the shielding eff ectiveness (SE) has been observed to improve with the increasein CNF’s loading in the polymer matrix. The SE is also a function of frequency, which is attributed to the increase in theskin depth. A SE of 20 dB has been estimated in these samples for the frequencies 1 THz and higher, which is of signifi cantimportance for the use of this technique in practical applications.
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.