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On the Reducibility of Appell's Function F4

Published online by Cambridge University Press:  20 November 2018

H. M. Srivastava
H. M. Srivastava*
Affiliation:
University of Victoria, Victoria, British Columbia
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Put

1

For the Appell function F4 defined by [3, p. 224]

2

Saxena [5, p. 216] proved a reduction formula in the form

3

where

It may be of interest to point out that formula (3) is not correct. Indeed we first establish the following general result.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 2 , June 1973 , pp. 295 - 298
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Burchnall, J. L., Differential equations associated with hypergeometric functions, Quart. J. Math. Oxford Ser. 13 (1942), 90–106.Google Scholar
2. Burchnall, J. L. and Chaundy, T. W., Expansions ofAppell’s double hypergeometric functionsߞ II, Quart. J. Math. Oxford Ser. 12 (1941), 112–128.Google Scholar
3. Erdélyi, A. et al., Higher transcendental functions, Vol. I, McGraw-Hill, New York, 1953.Google Scholar
4. Gupta, K. C., A reduction formula for Appell’s function F4 , Ganita. 15 (1965), 81–82.Google Scholar
5. Saxena, R. K., On the reducibility of Appell’s function F4 , Canad. Math. Bull. 9 (1966), 215–222.Google Scholar
6. Srivastava, H. M., Certain pairs of inverse series relations, J. Reine Angew. Math. 245 (1970), 47–54.Google Scholar