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Certain Summation Formulae for Basic Hypergeometric Series

Published online by Cambridge University Press:  20 November 2018

Arun Verma*
Affiliation:
Department of Mathematics, Lucknow University, Lucknow (India)
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In 1927, Jackson [5] obtained a transformation connecting a

where N is any integer, with a

viz.,

1

where | q | > l and |qγ-α-βN| > l.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Andrews, G. E., Subba Rao, M. V., and Vidya Sagar, M., A family of combinational Identities. Bull. Canadian Math. Soc. 15 (1972), 11-18.Google Scholar
2. Bailey, W. N., Identities of the Roger-Ramanujan type. Proc. London Math. Soc. (2) 50 (1949), 1-10.Google Scholar
3. Fox, C., The expansion of hypergeometric series in terms of similar series. Proc. London Math. Soc. (2) 26 (1927), 201-210.Google Scholar
4. Jackson, F. H., Transformations of q-series. Mess, of Math. 39 (1910), 145-153.Google Scholar
5. Jackson, F. H., A new transformation of Heinean series. Quart. Jour. Math. 50 (1927), 377-384.Google Scholar
6. Karlsson, Per. W., Hypergeometric functions with integral parameter differences. Jour. Math. Phys. 12 (1971), 270-271.Google Scholar
7. Lakin, A., A hypergeometric identity related to DougalVs theorem. Jour. London Math. Soc. 27 (1952), 229-234.Google Scholar
8. Sears, D. B., On the transformation theory of basic hypergeometric functions. Proc. London Math. Soc. (2) 53 (1951), 158-180.Google Scholar
9. Slater, L. J., Generalised hypergeometric series. Cambridge University Press (1966).Google Scholar