JOURNAL BROWSE
Search
Advanced SearchSearch Tips
GENERALIZED DOUBLE INTEGRAL INVOLVING KAMPÉ DE FÉRIET FUNCTION
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 33, Issue 1,  2011, pp.43-50
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2011.33.1.043
 Title & Authors
GENERALIZED DOUBLE INTEGRAL INVOLVING KAMPÉ DE FÉRIET FUNCTION
Kim, Yong-Sup; Ali, Shoukat; Rathie, Navratna;
  PDF(new window)
 Abstract
The aim of this paper is to obtain twenty five Eulerian type double integrals in the form of a general double integral involving Kamp de Friet function. The results are derived with the help of the generalized classical Watson`s theorem obtained earlier by Lavoie, Grondin and Rathie. A few interesting special cases of our main result are also given.
 Keywords
Kamp de Friet function;Watson`s theorem;double integral;
 Language
English
 Cited by
 References
1.
C. Adiga and T. Kim, On a generalization of Sandor's function, Proc. Jangjeon Math. Soc.5(2)(2002), 119-129.

2.
P. Appell et J. Kampe de Feriet, Fonctions Hypergeometriques et Hyper-spheriques Polynomes d'Hermite, Gauthier-Villars, Paris, 1926.

3.
J. Choi, A. K. Rathie, and H. Harsh, Remarks on a summation formula for three variables hypergeometric function $X_8$ and certain hypergeometric transformations, East Asian Math. J. 25(4)(2009), 481-486.

4.
J. Edward, A treatise on the integral calculus, Vol. II, Chelsea Publishing Company, New York,1922.

5.
H. Exton, hypergeometric functions of three variables , J. Indian acad. Math. 4(1982), 113-119.

6.
T. Kim, M. S. M. Naika, S. C. Kumar, L. C. Jang, Y. H. Kim and B. Lee, On some new Schlafli-type cubic modular equations, Adv. Stud. Contemp. Math. 20(1)(2010), 63-80.

7.
Y. S. Kim, J. Choi, and A. K. Rathie, Remark on two results by Padmanabham for Exton's triple hypergeometric series $X_8$, Honam Math. J. 27(4)(2005), 603-608.

8.
Y. S. Kim and A. K. Rathie, On an extension formula for the triple hypergeometric series $X_8$ due to Exton, Bull. Korean Math. Soc. 44(4)(2007), 743-751. crossref(new window)

9.
Y. S. Kim and A. K. Rathie, Another method for Padmanabham's transformation formula for Exton's triple hypergeometric series X8 for On an extension formula for the triple hypergeometric series X8, Commun. Korean Math. Soc. 24(4)(2009), 517-521. crossref(new window)

10.
J. L. Lavoie, F. Grondin and A. K. Rathie Generalizations of Watson's theorem on the sum of a $_3F_2$, Indian J. Math., 32(1)(1992), 23-32.

11.
S. W. Lee and Y. S. Kim, An extension of the triple hypergeometric series by Exton, Honam Math. J. 32(1)(2010), 61-71. crossref(new window)

12.
H. M. Srivastava and P. W. Karlsson(1985), Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester); Wiley, New York, Chichester, Brisbane, and Toronto.

13.
Z. Zhang and Y. Zhang, Summation formulas of q-series by modified Abel's lemma, Adv. Stud. Contemp. Math.17(2)(2008), 119-129.