On a new class of double integrals involving Gauss's ${}_{2}F_{1}$ hypergeometric function

  • Sungtae Jun Konkuk University

Abstract

In this paper, one hundred interesting double integrals involving Gauss's hypergeometric function in the form of four general integrals (twenty five each) have been evaluated in terms of gamma function. More than two hundred special cases have also been given.

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References

Bailey, W. N., Generalized Hypergeometric Series, Cambridge University Press, Cambridge, (1935); Re-printed by Stechert-Hafner, New York (1964).

Edwards, J., A Treaties on the Integral Calculus with Applications, Examples and Problems, Vol. II, Chelsea Publishing Campany, New York, (1954).

Jun, S., Kilicman, A., Kim, I., and Rathie, A. K., A class of double integral involving Gauss’s hypergeometric function, Submitted for publication, (2018).

Kim, I., Jun, S., Vyas, Y. and Rathie, A. K., On an extension of Edwards’s double integral with applications, Submitted for publication, (2018).

Lavoie, J. L., Grondin, F. and Rathie, A. K., Generalizations of Watson’s theorem on the sum of a 3F2, Indian J. Math., 34, (1992), 23-32.

Prudnikov, A. P., Brychkov, Yu. A., and Marichev, O.I., Integrals and Serie, Vol. 3, More Special Functions, Gordon and Breach Science Publishers, New York, (1990).

Rainville, E. D., Special Functions, The Macmillan Company, New York, (1960); Re-printed by Chelsea Publishing Company, Bronx, New York, (1971).

Rathie, A. K., Choi, J., Kim, Y. S. and Chajjer, G. C., On a new class of double integrals involving hypergeometric functions, Kyungpook Math. J. 39(2), (1999), 293-302.

Sylvester, J. J., The Collected Mathematical Papers, Vol. II, p.214 (footnote), Chelsea, New York, (1973).

Published
2020-10-11
Section
Articles