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FORMULAS DEDUCIBLE FROM A GENERALIZATION OF GOTTLIEB POLYNOMIALS IN SEVERAL VARIABLES
Choi, Junesang The Honam Mathematical Society 2012 호남수학학술지 Vol.34 No.4
Gottlieb polynomials were introduced and investigated in 1938, and then have been cited in several articles. Very recently Khan and Akhlaq introduced and investigated Gottlieb polynomials in two and three variables to give their generating functions. Subsequently, Khan and Asif investigated the generating functions for the $q$-analogue of Gottlieb polynomials. In this sequel, by modifying Khan and Akhlaq's method, Choi presented a generalization of the Gottlieb polynomials in $m$ variables to present two generating functions of the generalized Gottlieb polynomials ${\varphi}^m_n({\cdot})$. Here, we show that many formulas regarding the Gottlieb polynomials in m variables and their reducible cases can easily be obtained by using one of two generating functions for Choi's generalization of the Gottlieb polynomials in m variables expressed in terms of well-developed Lauricella series $F^{(m)}_D[{\cdot}]$.
ON A NEW CLASS OF SERIES IDENTITIES
( Nidhi Shekhawat ),( Junesang Choi ),( Arjun K. Rathie ),( Om Prakash ) 호남수학회 2015 호남수학학술지 Vol.37 No.3
We aim at giving explicit expressions of sum _{m,n=0} ^{INF } {△ _{m+n(-1) ^{n} x ^{m+n}}} over {(p) _{m} (p+i) _{n} m!n! ^{,}} where i = 0; §1; : : : ; §9 and f¢ng is a bounded sequence of com- plex numbers. The main result is derived with the help of the gen- eralized Kummer``s summation theorem for the series 2F1 obtained earlier by Choi. Further some special cases of the main result con- sidered here are shown to include the results obtained earlier by Kim and Rathie and the identity due to Bailey.
ON A NEW CLASS OF SERIES IDENTITIES
SHEKHAWAT, NIDHI,CHOI, JUNESANG,RATHIE, ARJUN K.,PRAKASH, OM The Honam Mathematical Society 2015 호남수학학술지 Vol.37 No.3
We aim at giving explicit expressions of $${\sum_{m,n=0}^{{\infty}}}{\frac{{\Delta}_{m+n}(-1)^nx^{m+n}}{({\rho})_m({\rho}+i)_nm!n!}$$, where i = 0, ${\pm}1$, ${\ldots}$, ${\pm}9$ and $\{{\Delta}_n\}$ is a bounded sequence of complex numbers. The main result is derived with the help of the generalized Kummer's summation theorem for the series $_2F_1$ obtained earlier by Choi. Further some special cases of the main result considered here are shown to include the results obtained earlier by Kim and Rathie and the identity due to Bailey.
SOME INTEGRAL REPRESENTATIONS OF THE CLAUSEN FUNCTION Cl<sub>2</sub>(x) AND THE CATALAN CONSTANT G
Choi, Junesang The Youngnam Mathematical Society 2016 East Asian mathematical journal Vol.32 No.1
The Clausen function $Cl_2$(x) arises in several applications. A large number of indefinite integrals of logarithmic or trigonometric functions can be expressed in closed form in terms of $Cl_2$(x). Very recently, Choi and Srivatava [3] and Choi [1] investigated certain integral formulas associated with $Cl_2$(x). In this sequel, we present an interesting new definite integral formula for the Clausen function $Cl_2$(x) by using a known relationship between the Clausen function $Cl_2$(x) and the generalized Zeta function ${\zeta}$(s, a). Also an interesting integral representation for the Catalan constant G is considered as one of two special cases of our main result.
CERTAIN NEW INTEGRAL FORMULAS INVOLVING THE GENERALIZED BESSEL FUNCTIONS
Choi, Junesang,Agarwal, Praveen,Mathur, Sudha,Purohit, Sunil Dutt Korean Mathematical Society 2014 대한수학회보 Vol.51 No.4
A remarkably large number of integral formulas involving a variety of special functions have been developed by many authors. Also many integral formulas involving various Bessel functions have been presented. Very recently, Choi and Agarwal derived two generalized integral formulas associated with the Bessel function $J_{\nu}(z)$ of the first kind, which are expressed in terms of the generalized (Wright) hypergeometric functions. In the present sequel to Choi and Agarwal's work, here, in this paper, we establish two new integral formulas involving the generalized Bessel functions, which are also expressed in terms of the generalized (Wright) hypergeometric functions. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.
SOME INTEGRAL TRANSFORMS INVOLVING EXTENDED GENERALIZED GAUSS HYPERGEOMETRIC FUNCTIONS
Choi, Junesang,Kachhia, Krunal B.,Prajapati, Jyotindra C.,Purohit, Sunil Dutt Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.4
Using the extended generalized integral transform given by Luo et al. [6], we introduce some new generalized integral transforms to investigate such their (potentially) useful properties as inversion formulas and Parseval-Goldstein type relations. Classical integral transforms including (for example) Laplace, Stieltjes, and Widder-Potential transforms are seen to follow as special cases of the newly-introduced integral transforms.
AN EXTENSION OF THE WHITTAKER FUNCTION
Choi, Junesang,Nisar, Kottakkaran Sooppy,Rahman, Gauhar Korean Mathematical Society 2021 대한수학회논문집 Vol.36 No.4
The Whittaker function and its diverse extensions have been actively investigated. Here we aim to introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function 𝚽<sub>p,v</sub> and investigate some of its formulas such as integral representations, a transformation formula, Mellin transform, and a differential formula. Some special cases of our results are also considered.
FURTHER LOG-SINE AND LOG-COSINE INTEGRALS
Junesang Choi 충청수학회 2013 충청수학회지 Vol.26 No.4
Motivated essentially by their potential for applica- tions in a wide range of mathematical and physical problems, the log-sine and log-cosine integrals have been evaluated, in the exist-ing literature on the subject, in many di??erent ways. Very recently, Choi [6] presented explicit evaluations of some families of log-sine and log-cosine integrals by making use of the familiar Beta func-tion. In the present sequel to the investigation [6], we evaluate the log-sine and log-cosine integrals involved in more complicated integrands than those in [6], by also using the Beta function.
Choi, Junesang,Shine, Raj S.N.,Rathie, Arjun K. The Youngnam Mathematical Society 2015 East Asian mathematical journal Vol.31 No.1
We use some known contiguous function relations for $_2F_1$ to show how simply the following three recurrence relations for Jacobi polynomials $P_n^{({\alpha},{\beta)}(x)$: (i) $({\alpha}+{\beta}+n)P_n^{({\alpha},{\beta})}(x)=({\beta}+n)P_n^{({\alpha},{\beta}-1)}(x)+({\alpha}+n)P_n^{({\alpha}-1,{\beta})}(x);$ (ii) $2P_n^{({\alpha},{\beta})}(x)=(1+x)P_n^{({\alpha},{\beta}+1)}(x)+(1-x)P_n^{({\alpha}+1,{\beta})}(x);$ (iii) $P_{n-1}^{({\alpha},{\beta})}(x)=P_n^{({\alpha},{\beta}-1)}(x)+P_n^{({\alpha}-1,{\beta})}(x)$ can be established.
Junesang Choi 경남대학교 기초과학연구소 2022 Nonlinear Functional Analysis and Applications Vol.27 No.1
There have been provided a surprisingly large number of summation formulae for generalized hypergeometric functions and series incorporating a variety of elementary and special functions in their various combinations. In this paper, we aim to consider certain generalized hypergeometric function 3F2 with particular arguments, through which a number of summation formulas for p+1Fp(1) are provided. We then establish a power series whose coefficients are involved in generalized hypergeometric functions with unit argument. Also, we demonstrate that the generalized hypergeometric functions with unit argument mentioned before may be expressed in terms of Bell polynomials. Further, we explore several special instances of our primary identities, among numerous others, and raise a problem that naturally emerges throughout the course of this investigation.