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Certain integral representations for the Riemann Zeta function ζ (s) at positive integer argument
( Junesang Choi ) 호남수학회 2013 호남수학학술지 Vol.35 No.4
We aim at presenting certain integral representations for the Riemann Zeta function ζ (s) positive integer arguments by using some known integral representations of log Γ(1+z) and ψ(1+z)
EXTENSION OF EXTENDED BETA, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS
( Junesang Choi ),( Arjun K. Rathie ),( Rakesh K. Parmar ) 호남수학회 2014 호남수학학술지 Vol.36 No.2
Recently several authors have extended the Gamma function, Beta function, the hypergeometric function, and the con-fluent hypergeometric function by using their integral representa-tions and provided many interesting properties of their extended functions. Here we aim at giving further extensions of the above-mentioned extended functions and investigating various formulas for the further extended functions in a systematic manner. More-over, our extension of the Beta function is shown to be applied to Statistics and also our extensions find some connections with other special functions and polynomials such as Laguerre polynomials, Macdonald and Whittaker functions.
CERTAIN NEW PATHWAY TYPE FRACTIONAL INTEGRAL INEQUALITIES
( Junesang Choi ),( Praveen Agarwal ) 호남수학회 2014 호남수학학술지 Vol.36 No.2
In recent years, diverse inequalities involving a vari-ety of fractional integral operators have been developed by many authors. In this sequel, here, we aim at establishing certain new inequalities involving pathway type fractional integral operator by following the same lines, recently, used by Choi and Agarwal [7]. Relevant connections of the results presented here with those earlier ones are also pointed out.
Decomposition formulas and integral representations for some Exton hypergeometric functions
Junesang Choi,Anvar Hasanov,Mamasali Turaev 충청수학회 2011 충청수학회지 Vol.24 No.4
Generalizing the Burchnall-Chaundy operator method, the authors are aiming at presenting certain decomposition formulas for the chosen six Exton functions expressed in terms of Appell's functions F_3 and F_4, Horn's functions H_3 and H_4, and Gauss's hypergeometric function F. We also give some integral representations for the Exton functions X_i (i=6, 8, 14)each of whose kernels contains the Horn's function H_4.
ON THE REDUCIBILITY OF KAMPE DE FERIET FUNCTION
( Junesang Choi ),( Arjun K. Rathie ) 호남수학회 2014 호남수학학술지 Vol.36 No.2
The main objective of this paper is to obtain a formula containing eleven interesting results for the reducibility of Kampe de Feriet function. The results are derived with the help of two general results for the series 2F1(2) very recently presented by Kim et al. Well known Kummer`s second theorem and its contiguous results proved earlier by Rathie and Nagar, and Kim et al. follow special cases of our main findings.
FUNCTIONAL RELATIONS INVOLVING SRIVASTAVA S HYPERGEOMETRIC FUNCTIONS HB AND F(3)
Junesang Choi,Anvar Hasanov,Mamasali Turaev 충청수학회 2011 충청수학회지 Vol.24 No.2
B. C. Carlson [Some extensions of Lardner s relations between 0F3 and Bessel functions, SIAM J. Math. Anal. 1(2) (1970), 232{242] presented several useful relations between Bessel and generalized hypergeometric functions that generalize some ear- lier results. Here, by simply splitting Srivastava s hypergeometric function HB into eight parts, we show how some useful and gener- alized relations between Srivastava s hypergeometric functions HB and F(3) can be obtained. These main results are shown to be spe- cialized to yield certain relations between functions 0F1, 1F1, 0F3,ª2, and their products including di??erent combinations with dif- ferent values of parameters and signs of variables. We also consider some other interesting relations between the Humbert ª2 function and Kamp¶e de F¶eriet function, and between the product of expo- nential and Bessel functions with Kamp¶e de F¶eriet functions.
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.
Certain unified integrals involving a product of Bessel functions of the first kind
( Junesang Choi ),( Praveen Agarwal ) 호남수학회 2013 호남수학학술지 Vol.35 No.4
A remarkably large number of integrals involving a product of certain combinations of Bessel functions of several kinds as well as Bessel functions, themselves, have been investigated by many authors. Motivated the works of \emph both Garg and Mittal and Ali, very recently, Choi and Agarwal gave two interesting unified integrals involving the Bessel function of the first kind Jv(z). In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present two generalized integral formulas involving a product of Bessel functions of the first kind, which are expressed in terms of the generalized Lauricella series due to Srivastava and Daoust. Some interesting special cases and (potential) usefulness of our main results are also considered and remarked, respectively.
Several Integral Representations Involving Triple Hypergeometric Functions
( Junesang Choi ),( Anvar Hasanov ),( Mamasali Turaev ) 호남수학회 2011 호남수학학술지 Vol.33 No.2
A (presumably) new class of generalized triple hyper-geometric functions is presented. We also give integral representa-tions of Laplace type for certain special cases of the new class offunctions.
( Junesang Choi ),( Sanjib Kumar Datta ),( Tanmay Biswas ),( Md Nazimul Islam ) 호남수학회 2017 호남수학학술지 Vol.39 No.1
In this paper, we aim to prove certain common fixed point theorems for a pair of weakly compatible mappings satisfying (CLRg) (or (E.A)) property in the bicomplex valued metric spaces. We also provide some examples which support the main results here.