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On the Reducibility of Appelles Function F4*

Published online by Cambridge University Press:  20 November 2018

R.K. Saxena
R.K. Saxena*
Affiliation:
McGill University
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It is a well-known fact in the theory of Appell's hypergeometric function of two variables F4, defined by

1

where |x|1/2 + |y|1/2 < 1, that it can be expressed interms of products of ordinary hypergeometric functions when γ + γ' = α + β + 1.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 2 , June 1966 , pp. 215 - 222
Copyright
Copyright © Canadian Mathematical Society 1966

Footnotes

*

Supported by a Post-doctorate fellowship of the National Research Council of Canada.

References

1. Bailey, W.N., A reducible case of the fourth type of Appell's hypergeometric function of two variables, Quart. Jour, of Math. (Oxford), Vol. 4(1933), 305-308.Google Scholar
2. Bailey, W.N., On the reducibility of Appell's function F4 , Quart. Jour, of Math. (Oxford), vol.5 (1936)291-292.Google Scholar
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5. Erdelyi, A., et al. Tables of integral transforms, vol.1, McGraw-Hill, New York (1954).Google Scholar
6. Erdelyi, A., et al. Tables of integral transforms, vol.2, McGraw Hill, New York (1954).Google Scholar
7. Saxena, R.K., Integrals involving products of Bessel functions, Proc. Glasgow Mathematical Assoc. vol.6, (1964), 130-132.Google Scholar
8. Saxena, R.K., Integrals involving Bessel functions and Whittaker functions, Proc. Cambridge Philosophical Soc. vol.60, (1960), 174-176.Google Scholar