Browse > Article
http://dx.doi.org/10.7468/jksmeb.2018.25.1.7

A NOTE ON CERTAIN LAPLACE TRANSFORMS FOR THE GENERALIZED HYPERGEOMETRIC FUNCTION 3F3  

Kim, Insuk (Department of Mathematics Education, Wonkwang University)
Jun, Sungtae (General education Institute, Konkuk University)
Publication Information
The Pure and Applied Mathematics / v.25, no.1, 2018 , pp. 7-16 More about this Journal
Abstract
The main objective of this paper is to demonstrate how one can obtain very quickly so far unknown Laplace transforms of rather general cases of the generalized hypergeometric function $_3F_3$ by employing generalizations of classical summation theorems for the series $_3F_2$ available in the literature. Several new as well known results obtained earlier by Kim et al. follow special cases of main findings.
Keywords
hypergeometric functions; classical summation theorems; integral representation for $_2F_1$;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 J.L. Lavoie, F. Grondin & A.K. Rathie: Generalizations of Whipple's theorem on the sum of a $_3F_2$. J. Comput. Appl. Math. 72 (1996), 293-300.   DOI
2 E.D. Rainville: Special Functions. Macmillan, New York, 1960; Re-printed by Chelsea Publishing Company, Brox, New York, 1971.
3 L.J. Slater: Generalized Hypergeometric Functions. Cambridge University Press, Cambridge, 1966.
4 H.M. Srivastava & J. Choi: Zeta and q-zeta Functions and Associated Series and Integrals. Elsevier Science Publishers, Amsterdam, London and New York, 2012.
5 W.N. Bailey: Generalized Hypergeometric Series. Cambridge University Press, Cambridge, 1935; Re-printed by Stechert-Hafner, New York, 1964.
6 J. Choi & A.K. Rathie: On several new general Laplace transforms for generalized hypergeometric functions $_1F_1$(a; b; x). Submitted for publication, (2016).
7 B. Davis: Integral Transforms and Their Applications. Third ed., Springer, New York, 2002.
8 G. Doetsch: Introduction to the theory and application of Laplace transformations. Springer, New York, 1974.
9 A. Erdelyi, W. Magnus, F. Oberhettinger & F.G. Tricom: Tables of Integral Trans-forms. Vol. I and II, McGraw Hills, New York, 1954.
10 Y.S. Kim, A.K. Rathie & D. Cvijovic: New Laplace transforms of Kummer's conuent hypergeometric functions. Math. Comp. Modelling 50 (2002), 1068-1071.
11 Y.S. Kim, A.K. Rathie & C.H. Lee: New Laplace transforms for the generalized hypergeometric function $_2F_2$. Honam Math. J. 37 (2015), no. 2, 245-252.   DOI
12 J.L. Lavoie, F. Grondin & A.K. Rathie: Generalizations of Watson's theorem on the sum of a $_3F_2$. Indian J. Math. 34 (1992), 23-32.
13 J.L. Lavoie, F. Grondin, A.K. Rathie & K. Arora: Generalizations of Dixon's theorem on the sum of a $_3F_2$. Math. Comp. 62 (1994), 267-276.