


Paper's Title:
Two Further Methods for Deriving Four Results Contiguous to Kummer's Second Theorem
Author(s):
I. Kim and J. Kim
Department of Mathematics Education,
Wonkwang University,
Iksan, 570749,
Korea.
Email: iki@wku.ac.kr
Department of Mathematics Education,
Wonkwang University,
Iksan, 570749,
Korea.
Email: joohyung@wku.ac.kr
Abstract:
In the theory of generalized hypergeometric function, transformation and summation formulas play a key role. In particular, in one of the Kummer's transformation formulas, Kim, et al. in 2012, have obtained ten contiguous results in the form of a single result with the help of generalization of Gauss's second summation theorem obtained earlier by Lavoie, et al.. In this paper, we aim at presenting four of such results by the technique of contiguous function relations and integral method developed by MacRobert.
Paper's Title:
On a New Class of Eulerian's Type Integrals Involving Generalized Hypergeometric Functions
Author(s):
Sungtae Jun, Insuk Kim and Arjun K. Rathie
General Education Institute,
Konkuk University, Chungju 380701,
Republic of Korea.
Department of Mathematics Education,
Wonkwang University, Iksan, 570749,
Republic of Korea.
Department of Mathematics,
Vedant College of Engineering and Technology (Rajasthan Technical University),
Bundi323021, Rajasthan,
India.
Email: sjun@kku.ac.kr, iki@wku.ac.kr, arjunkumarrathie@gmail.com
Abstract:
Very recently MasjedJamei and Koepf established interesting and useful generalizations of various classical summation theorems for the _{2}F_{1}, _{3}F_{2}, _{4}F_{3}, _{5}F_{4} and _{6}F_{5} generalized hypergeometric series. The main aim of this paper is to establish eleven Eulerian's type integrals involving generalized hypergeometric functions by employing these theorems. Several special cases have also been given.
Paper's Title:
On an extension of Edwards's double integral with applications
Author(s):
I. Kim, S. Jun, Y. Vyas and A. K. Rathie
Department of Mathematics Education,
Wonkwang University,
Iksan, 570749,
Republic of Korea.
General Education Institute,
Konkuk University,
Chungju 380701,
Republic of Korea.
Department of Mathematics, School of
Engineering,
Sir Padampat Singhania University,
Bhatewar, Udaipur, 313601, Rajasthan State,
India.
Department of Mathematics,
Vedant College of Engineering and Technology,
(Rajasthan Technical University),
Bundi323021, Rajasthan,
India.
Email: iki@wku.ac.kr
sjun@kku.ac.kr
yashoverdhan.vyas@spsu.ac.in
arjunkumarrathie@gmail.com
Abstract:
The aim of this note is to provide an extension of the well known and useful Edwards's double integral. As an application, new class of twelve double integrals involving hypergeometric function have been evaluated in terms of gamma function. The results are established with the help of classical summation theorems for the series _{3}F_{2} due to Watson, Dixon and Whipple. Several new and interesting integrals have also been obtained from our main findings.
Paper's Title:
Evaluation of a New Class of Double Integrals Involving Generalized Hypergeometric Function _{4}F_{3}
Author(s):
Joohyung Kim, Insuk Kim and Harsh V. Harsh
Department of Mathematics Education,
Wonkwang University, Iksan, 570749,
Korea.
Email: joohyung@wku.ac.kr
Department of Mathematics Education,
Wonkwang University, Iksan, 570749,
Korea.
Email: iki@wku.ac.kr
Department of Mathematics, Amity School
of Eng. and Tech.,
Amity University Rajasthan
NH11C, Jaipur303002, Rajasthan,
India.
Email: harshvardhanharsh@gmail.com
Abstract:
Very recently, Kim evaluated some double integrals involving a generalized hypergeometric function _{3}F_{2} with the help of generalization of Edwards's wellknown double integral due to Kim, et al. and generalized classical Watson's summation theorem obtained earlier by Lavoie, et al. In this research paper we evaluate one hundred double integrals involving generalized hypergeometric function _{4}F_{3} in the form of four master formulas (25 each) viz. in the most general form for any integer. Some interesting results have also be obtained as special cases of our main findings.
Paper's Title:
Several New Closedform Evaluations of the Generalized Hypergeometric Function with Argument 1/16
Author(s):
B. R. Srivatsa Kumar, Insuk Kim and Arjun K. Rathie
Department of Mathematics,
Manipal Institute of Technology,
Manipal Academy of Higher Education,
Manipal 576 104,
India.
Email: sri_vatsabr@yahoo.com
Department of Mathematics Education,
Wonkwang University,
Iksan, 54538,
Republic of Korea.
Email: iki@wku.ac.kr
Department of Mathematics,
Vedant College of Engineering and Technology,
Rajasthan Technical University,
Bundi, 323021, Rajasthan,
India.
Email: arjunkumarrathie@gmail.com
Abstract:
The main objective of this paper is to establish as many as thirty new closedform evaluations of the generalized hypergeometric function _{q+1}F_{q}(z) for q= 2, 3, 4. This is achieved by means of separating the generalized hypergeometric function _{q+1}F_{q}(z) for q=1, 2, 3, 4, 5 into even and odd components together with the use of several known infinite series involving central binomial coefficients obtained earlier by Ji and Hei \& Ji and Zhang.
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