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SOME INTEGRALS ASSOCIATED WITH MULTIINDEX MITTAG-LEFFLER FUNCTIONS
Nabiullah Khan,Talha Usman,M. Ghayasuddin 한국전산응용수학회 2016 Journal of applied mathematics & informatics Vol.34 No.3
The object of the present paper is to establish two interesting unified integral formulas involving Multiple (multiindex) Mittag-Leffler functions, which is expressed in terms of Wright hypergeometric function. Some deduction from these results are also considered.
GENERALIZATION OF EXTENDED APPELL`S AND LAURICELLA`S HYPERGEOMETRIC FUNCTIONS
( N U Khan ),( M Ghayasuddin ) 호남수학회 2015 호남수학학술지 Vol.37 No.1
Recently, Liu and Wang generalized Appell’s and Lau-ricella’s hypergeometric functions. Motivated by the work of Liu and Wang, the main object of this paper is to present new gen-eralizations of Appell’s and Lauricella’s hypergeometric functions. Some integral representations, transformation formulae, di erential formulae and recurrence relations are obtained for these new gen-eralized Appell’s and Lauricella’s functions.
A NEW CLASS OF PARTIALLY DEGENERATE LAGUERRE-BASED HERMITE-GENOCCHI POLYNOMIALS
Waseem A. Khan,M. GHAYASUDDIN,DIVESH SRIVASTAVA 장전수학회 2022 Advanced Studies in Contemporary Mathematics Vol.32 No.1
In this paper, we introduce partially degenerate Laguerre- based Hermite-Genocchi and investigate their properties and identities. Furthermore, we introduce a generalized form of partially degenerate Laguerre-based Hermite-Genocchi and derive some interesting proper- ties and identities. The results obtained are of general character and can be reduced to yield formulas and identities for relatively simple polyno- mials and numbers.
GENERALIZATION OF EXTENDED APPELL'S AND LAURICELLA'S HYPERGEOMETRIC FUNCTIONS
Khan, N.U.,Ghayasuddin, M. The Honam Mathematical Society 2015 호남수학학술지 Vol.37 No.1
Recently, Liu and Wang generalized Appell's and Lauricella's hypergeometric functions. Motivated by the work of Liu and Wang, the main object of this paper is to present new generalizations of Appell's and Lauricella's hypergeometric functions. Some integral representations, transformation formulae, differential formulae and recurrence relations are obtained for these new generalized Appell's and Lauricella's functions.
ON INTEGRAL OPERATORS INVOLVING THE PRODUCT OF GENERALIZED BESSEL FUNCTION AND JACOBI POLYNOMIAL
WASEEM A. KHAN,M. GHAYASUDDIN,DIVESH SRIVASTAVA 한국전산응용수학회 2018 Journal of applied mathematics & informatics Vol.36 No.5
The aim of this research note is to evaluate two generalized integrals involving the product of generalized Bessel function and Jacobi polynomial by employing the result of Obhettinger [2]. Also, by mean of the main results, we have established an interesting relation in between Kampe de Feriet and Srivastava and Daoust functions. Some interesting special cases of our main results are also indicated.
CERTAIN NEW EXTENSION OF HURWITZ-LERCH ZETA FUNCTION
WASEEM A. KHAN,M. GHAYASUDDIN,Moin Ahmad 한국전산응용수학회 2019 Journal of applied mathematics & informatics Vol.37 No.1
In the present research paper, we introduce a further exten- sion of Hurwitz-Lerch zeta function by using the generalized extended Beta function dened by Parmar et al. [9]. We investigate its integral represen- tations, Mellin transform, generating functions and dierential formula. In view of diverse applications of the Hurwitz-Lerch Zeta functions, the results presented here may be potentially useful in some related research areas.
ON INTEGRAL OPERATORS INVOLVING THE PRODUCT OF GENERALIZED BESSEL FUNCTION AND JACOBI POLYNOMIAL
KHAN, WASEEM A.,GHAYASUDDIN, M.,SRIVASTAVA, DIVESH The Korean Society for Computational and Applied M 2018 Journal of applied mathematics & informatics Vol.36 No.5
The aim of this research note is to evaluate two generalized integrals involving the product of generalized Bessel function and Jacobi polynomial by employing the result of Obhettinger [2]. Also, by mean of the main results, we have established an interesting relation in between $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ and Srivastava and Daoust functions. Some interesting special cases of our main results are also indicated.
CERTAIN NEW EXTENSION OF HURWITZ-LERCH ZETA FUNCTION
KHAN, WASEEM A.,GHAYASUDDIN, M.,AHMAD, MOIN The Korean Society for Computational and Applied M 2019 Journal of applied mathematics & informatics Vol.37 No.1
In the present research paper, we introduce a further extension of Hurwitz-Lerch zeta function by using the generalized extended Beta function defined by Parmar et al.. We investigate its integral representations, Mellin transform, generating functions and differential formula. In view of diverse applications of the Hurwitz-Lerch Zeta functions, the results presented here may be potentially useful in some related research areas.
SOME INTEGRALS ASSOCIATED WITH MULTIINDEX MITTAG-LEFFLER FUNCTIONS
KHAN, N.U.,USMAN, T.,GHAYASUDDIN, M. The Korean Society for Computational and Applied M 2016 Journal of applied mathematics & informatics Vol.34 No.3
The object of the present paper is to establish two interesting unified integral formulas involving Multiple (multiindex) Mittag-Leffler functions, which is expressed in terms of Wright hypergeometric function. Some deduction from these results are also considered.