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http://dx.doi.org/10.5831/HMJ.2015.37.2.245

NEW LAPLACE TRANSFORMS FOR THE GENERALIZED HYPERGEOMETRIC FUNCTION 2F2  

KIM, YONG SUP (Department of Mathematics Education, Wonkwang University)
RATHIE, ARJUN K. (Department of Mathematics, School of Mathematical and Physical Science, Central University of Kerala Riverside Transit Campus)
LEE, CHANG HYUN (Department of Medicine, Seonam University)
Publication Information
Honam Mathematical Journal / v.37, no.2, 2015 , pp. 245-252 More about this Journal
Abstract
This paper is in continuation of the paper very recently published [New Laplace transforms of Kummer's confluent hypergeometric functions, Math. Comp. Modelling, 55 (2012), 1068-1071]. In this paper, our main objective is to show one can obtain so far unknown Laplace transforms of three rather general cases of generalized hypergeometric function $_2F_2(x)$ by employing generalized Watson's, Dixon's and Whipple's summation theorems for the series $_3F_2$ obtained earlier in a series of three research papers by Lavoie et al. [5, 6, 7]. The results established in this paper may be useful in theoretical physics, engineering and mathematics.
Keywords
Confluent hypergeometric function; Laplace transform; Gauss's summation theorem; Kummer's summation theorem;
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  • Reference
1 B. Davies, Integral transforms and their applications, third ed. Springer, New york, 2002.
2 G. Doetsch, Introduction to the theory and applications of Laplace transformation, Springer, New york, 1974.
3 A. Erdelyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Tables of Integral transforms, Vol. I, II, McGraw Hill, New york, 1954.
4 Y.S. Kim, A.K. Rathie and D. Cvijovic, New Laplace transforms of Kummer's confluent hypergeometric functions, Math. Comp. Modelling 55 (2012), 1068-1071.   DOI
5 J.L. Lavoie, F. Grondin and A.K. Rathie, Generalizations of Watson's theorem on the sum of a $_{3}F_{2}$, Indian J. Math. 34 (1992), 23-32.
6 J.L. Lavoie, F. Grondin, A.K. Rathie and K. Arora, Generalizations of Dixon's theorem on the sum of a $_{3}F_{2}$, Math. Comp. 62 (1994), 267-276.
7 J.L. Lavoie, F. Grondin and A.K. Rathie, Generalizations of Whipple's theorem on the sum of a $_{3}F_{2}$, J. Comp. 72 (1996), 293-300.
8 F. Oberhettinger and L. Badi, Tables of Laplace transforms, Springer, Berlin, 1973.
9 A.P. Prudnikov, Yu.A. Brychkov and O. I. Marichev, Integrals and series: Direct Laplace transforms, Vol. 4, Gordon and Breach science publishers, New York, 1992.
10 E.D. Rainville, Special functions, Macmillan, New York, 1960.
11 L.J. Slater, Generalized hypergeometric functions, Cambridge University press, Cambridge, 1966.
12 H.M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated series and Integrals, Elsvier Science Publishers, Amsterdam, London and New York, (2012).