## Taiwanese Journal of Mathematics

### A GENERAL THEOREM FOR THE GENERALIZED WEYL FRACTIONAL INTEGRAL OPERATOR INVOLVING THE MULTIVARIABLE H-FUNCTION

#### Abstract

In this paper we establish a very general and useful theorem which interconnects the Laplace transform and the generalized Weyl fractional integral operator involving the multivariable H-function of related functions of several variables. Our main theorem involves a multidimensional series with essentially arbitrary sequence of complex numbers. By suitably assigning different values to these sequences, one can easily evaluate the generalized Weyl fractional integral operator of special functions of several variables. We have illustrated it for Srivastava-Daoust multivariable hypergeometric function. On account of general nature of this function a number of results involving special functions of one or more variables can be obtained merely by specializing the parameters.

#### Article information

Source
Taiwanese J. Math., Volume 8, Number 4 (2004), 559-568.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500407704

Digital Object Identifier
doi:10.11650/twjm/1500407704

Mathematical Reviews number (MathSciNet)
MR2105552

Zentralblatt MATH identifier
1065.26011

#### Citation

Goyal, S. P.; Goyal, Ritu. A GENERAL THEOREM FOR THE GENERALIZED WEYL FRACTIONAL INTEGRAL OPERATOR INVOLVING THE MULTIVARIABLE H-FUNCTION. Taiwanese J. Math. 8 (2004), no. 4, 559--568. doi:10.11650/twjm/1500407704. https://projecteuclid.org/euclid.twjm/1500407704

#### References

• A. Erdélyi, et al., Tables of Integral Transforms, Vol. 1, McGraw-Hill, New York, 1954.
• S. P. Goyal and Goyal Ritu, A general theorem involving generalized (Weyl) fractional integral operator, Aligarh Bull. Math., 21 (2002), 45-55.
• S. P. Goyal and Rashmi Garg, On Laplace transform and Weyl fractional integral operator for one or more variables, Far East J. Math. Sci., 7 (2002), 269-283.
• R. Jain and M. A.Pathan, On Theorems involving Laplace Transform and Weyl Fractional Integral Operator, Proceedings of Second International Conference of Society for Special Functions and their Applications, (eds. R. Y. Denis, and M. A. Pathan), II (2001), 51-56.
• E. D. Rainville, Special Functions, Chelsea Publ. Comp. Bronx, New York, 1971.
• H. M. Srivastava and M. C. Daoust, Certain generalized Neumann expansions associated with the Kampé de Fériet function, Nederl. Akad. Wetensch. Proc. Ser., A 72 (1969), 449-457.
• H. M. Srivastava and M. C. Daoust, A note on the convergence of Kampé de Fériet double hypergeometric series, Math. Nachr., 53 (1972), 151-157.
• H. M. Srivastava, K. C. Gupta and S. P. Goyal, The $H$-Functions of One and Two Variables with Applications, South Asian Publishers, New Delhi and Madras, 1982.
• H. M. Srivastava and R. Panda, Some expansion theorems and generating relations for the H-function of several complex variables I and II, Comment. Math. Univ. St. Paul. 24 (1975), 119-137; ibid, 25 (1976), 167-197.
• Srivastava H. M. and Panda R., Some bilateral generating functions for a class of generalized hypergeometric polynomials, J. Reine Angew. Math., 283/284 (1976), 265-274.
• H. M. Srivastava and R. Panda, Certain multidimensional integral transformations I and II, Nederl. Akad. Wetensch. Proc. Ser., A81\! = \!Indag. Math., 40 (1978), 118-131 and 132-144.