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Partially degenerate poly-Bernoulli polynomials associated with Hermite polynomials
WASEEM A. KHAN,Moin Ahmad 장전수학회 2018 Advanced Studies in Contemporary Mathematics Vol.28 No.3
In this paper, we derive generating functions for the partially degenerate Hermite poly-Bernoulli polynomials and investigate some properties of these polynomials related to the Stirling numbers of the second kind. Further, we derive the summation formulae and general symmetry identities for that polynomials by using different analytical means on its generating function. Also, generating functions and summation formulae for the polynomials related to partially degenerate Hermite poly- Bernoulli polynomials are obtained as applications of main results.
A Note on $(p,q)$-analogue Type of Frobenius-Genocchi Numbers and Polynomials
Waseem A. Khan,Idrees A. Khan 영남수학회 2020 East Asian mathematical journal Vol.36 No.1
The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius-Genocchi numbers and polynomials of order α and inves- tigate some basic identities and properties for these polynomials and num- bers including addition theorems, difference equations, derivative proper- ties, recurrence relations. We also obtain integral representations, im- plicit and explicit formulas and relations for these polynomials and num- bers. Furthermore, we consider some relationships for Apostol type (p, q)- Frobenius-Genocchi polynomials of order α associated with (p, q)-Apostol Bernoulli polynomials, (p, q)-Apostol Euler polynomials and (p, q)-Apostol Genocchi polynomials.
A NEW CLASS OF GENERALIZED APOSTOL-TYPE FROBENIUS-EULER-HERMITE POLYNOMIALS
( M. A. Pathan ),( Waseem A. Khan ) 호남수학회 2020 호남수학학술지 Vol.42 No.3
In this paper, we introduce a new class of general-ized Apostol-type Frobenius-Euler-Hermite polynomials and derive some explicit and implicit summation formulae and symmetric iden- tities by using different analytical means and applying generating functions. These results extend some known summations and iden-tities of generalized Frobenius-Euler type polynomials and Hermite-based Apostol-Euler and Apostol-Genocchi polynomials studied by Pathan and Khan, Kurt and Simsek.
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.
A note on type 2 degenerate multi-poly-Bernoulli polynomials of the second kind
Waseem A. Khan,M. KAMARUJJAMA 장전수학회 2022 Proceedings of the Jangjeon mathematical society Vol.25 No.1
In this paper, we introduce type 2 degenerate multi-poly- Bernoulli polynomials of the second kind which are defined by using the degenerate multi polyexponential function. We investigate some prop- erties of those numbers and polynomials. Also, we give some identities and relations for the degenerate multi-poly-Bernoulli polynomials and numbers of the second.
A NEW CLASS OF TRICOMI-LEGENDRE-HERMITE-BERNOULLI POLYNOMIALS
Waseem A. Khan 장전수학회 2022 Advanced Studies in Contemporary Mathematics Vol.32 No.3
In this paper, we introduce a new class of generalized Tricomi- Legendre-Hermite-Bernoulli polynomials and consequently of Tricomi, Bernoulli, and Hermite polynomials and their generalizations start from suitable generating functions. These polynomials are used to connect Fubini-Legendre-Hermite and Bell-Legendre-Hermite polynomials and to find new representations. We derive some implicit summation for- mulae for these families of special functions by applying the generating 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.
A UNIFIED PRESENTATION OF BETA, GAUSS AND CONFLUENT HYPERGEOMETRIC FUNCTIONS
MOHD GHAYASUDDIN,MUSHARRAF ALI,Waseem A. Khan 장전수학회 2022 Advanced Studies in Contemporary Mathematics Vol.32 No.1
In this article, we propose a new extension of beta function by making use of the Bessel-Struve kernel function. Here, first we derive some fundamental properties of this function and then we present a new extension of beta distribution in terms of our proposed beta function. Furthermore, by using the definition of our new beta function, we introduce and investigate a new generalization of Gauss and con uent hypergeometric functions.
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.
ON HIGHER ORDER (p, q)-FROBENIUS-GENOCCHI NUMBERS AND POLYNOMIALS
Waseem A. Khan,Idrees A. Khan,J.Y. Kang 한국전산응용수학회 2019 Journal of applied mathematics & informatics Vol.37 No.3
In the present paper, we introduce (p, q)-Frobenius-Genocchi numbers and polynomials and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, implicit and explicit formulas and relations for these polynomials and numbers. We consider some relationships for (p, q)-Frobenius-Genocchi polynomials of order α associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials.