Operational Images and Relations of Two and Three Variables Hypergeometric Series

  • Maged Gumman Bin-Saad Department of Mathematics, Aden University, Aden, P.O.Box 6014 ,Yemen
  • Maisoon A. Hussein Department of Mathematics, Aden University, Aden, P.O.Box 6014, Yemen
Keywords: Formal operators Operational images, Appell's and Lauricella's hypergeometric functions, operational relations.

Abstract

Based upon the classical derivative and integral operators we introduce a new symbolic operational images for hypergeometric functions of two and three  variables. By means of these symbolic operational images a number of operational relations among the hypergeometric functions of two and three  variables are then found. Other closely-related results are also considered.

Downloads

Download data is not yet available.

References

Bin-Saad, Maged G. (2011). Symbolic operational images and decomposition formulas of hypergeometric functions. J. Math. Anal. Appl. ,376, 451–468.

Chen, M.P., Srivastava, H.M. (1997). Fractional calculus operators and their applications involving power functions and summation of series. Appl. Math. Comput., 81, 283-304.

Goyal, S.P., Jain, R.M., Gaur, N.(1992). Fractional integral operators involving a product of generalized hypergeometric functions and a general class of polynomials II. Indian J. Pure Appl. Math. ,23, 121-128.

Goyal, S.P. ,Jain, R.M. ,Gaur, N.(1991). Fractional integral operators involving a product of generalized hypergeometric functions and a general class of polynomials. Indian J. Pure Appl. Math., 22, 403-411.

Kalla, S.L. (1970).Integral operators of fractional integration. Mat. Notae 22,89-93.

Kalla, S.L.(1976) .Integral operators of fractional integration II .Mat. Notae 25, 29-35.

Kalla, S.L., Saxena, R. K.(1969). Integral operators involving hypergeometric functions. Math. Zeitschr.108 , 231-234.

Kalla, S.L., Saxena, R. K.(1974). Integral operators involving hypergeometric functions II. Univ. Nac. Tucuman Rev. Ser. A 24 , 31-36.

Kant, S., Koul, C.L.(1991). On fractional integral operators. J. Indian Math. Soc.(N.S) 56,97-107.

Ross, B., Fractional calculus and its applications(1975). Lecture Notes in Mathematics. Vol. 457, Springer- Verlag.

Srivastava, H.M. and Karlsson, P.W. (1985).Multiple Gaussian hypergeometric series. Halsted Press, Brisbane, New York and Toronto .

Tu, S.T. ,Chyan, D.-K., Srivastava, H.M.(1996). Certain operators of fractional calculus and their applications associated with logarithmic and Digamma functions. J. Fractional calculus 10, 67-73.

Published
2015-02-26
How to Cite
Bin-Saad, M., & Hussein, M. A. (2015). Operational Images and Relations of Two and Three Variables Hypergeometric Series. Journal of Progressive Research in Mathematics, 2(1), 39-46. Retrieved from https://scitecresearch.com/journals/index.php/jprm/article/view/46
Section
Articles