Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-12T02:09:54.966Z Has data issue: false hasContentIssue false
  • English
  • Français

Certain Summation Formulae for Basic Hypergeometric Series

Published online by Cambridge University Press:  20 November 2018

Arun Verma
Arun Verma*
Affiliation:
Department of Mathematics, Lucknow University, Lucknow (India)
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 3 , 01 September 1977 , pp. 369 - 375
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