Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T16:03:47.518Z Has data issue: false hasContentIssue false
  • English
  • Français

Some convolution identities based upon Ramanujan's bilateral sum

Published online by Cambridge University Press:  17 April 2009

H.M. Srivastava
H.M. Srivastava
Affiliation:
Department of Mathematics andStatistics University of VictoriaVictoria British Columbia V8W 3P4Canada
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.

Recently, Bhargava, Adiga and Somashekara made use of Ramanujan's 1Ψ1 summation formula to prove a convolution identity for certain coefficients generated by the quotient of two infinite products. As special cases of this identity, they deduced several results (connected especially with the generalised Frobenius partition functions) including, for example, the convolution identities given earlier by Kung-Wei Yang. In this sequel to the aforementioned works, we provide a complete answer to an interesting question raised by Bhargava, Adiga and Somashekara in connection with one class of their convolution identities.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 3 , June 1994 , pp. 433 - 437
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Bhargava, S., Adiga, C. and Somashekara, D.D., ‘Ramanujan's remarkable summation formula and an interesting convolution identity’, Bull. Austral. Math. Soc. 47 (1993), 155–162.Google Scholar
[2]Slater, L.J., Generalized hypergeometric functions (Cambridge University Press, Cambridge, London and New York, 1966).Google Scholar
[3]Yang, K.-W., ‘On the product (1+qnx+q2n x2)’, J. Austral. Math. Soc. Ser. A 48 (1990), 148–151.CrossRefGoogle Scholar