The Bhargava-Adiga Summation and Partitions

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Authors

  • George E. Andrews
     The Pennsylvania State University University Park, PA 16802 ,US

DOI:

https://doi.org/10.18311/jims/2017/15836

Keywords:

Bhargava-Adiga, Ramanujan, Compact Partitions, Self-Conjugate Partitions

Abstract

The Bhargava-Adiga summation rivals the 1ψ1􀀀summation of Ramanujan in elegance. This paper is devoted to two applications in the theory of integer partitions leading to partition questions related to Gauss's celebrated three triangle theorem.

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Published

2017-07-01

How to Cite

Andrews, G. E. (2017). The Bhargava-Adiga Summation and Partitions. The Journal of the Indian Mathematical Society, 84(3-4), 151–160. https://doi.org/10.18311/jims/2017/15836

Issue

Volume 84, Issue 3-4, July-December 2017

Section

Articles

License

Copyright (c) 2017 George E. Andrews

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2017-04-05
Accepted 2017-04-05
Published 2017-07-01

 

References

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S. Bhargava and C. Adiga, A basic bilateral series summation formula and its applications, Integral Transforms and Special Functions, 2 (1994), 165-184.

S. Bhargava, C. Adiga and D. D. Somashekara, Three square theorem as an application of Andrews' identity, Fibo. Quart., 31 (1993), 129-133.

N. J. Fine, Basic Hypergeometric Series and Applications, AMS Math. Surveys and Monographs, Vol. 27, Amer. Math. Soc., Providence, 1988.

N. J. A. Sloane, On-line Encyclopedia of Integer Sequences (OEIS), https://oeis.org.

D. D. Somashekara, K. N. Murthy and S. I. Shalini, On a new summation formula for 2 ψ 2 basic bilateral hypergeometric series and its applications, Int. J. Math. and Math.Sci., 2011 (2011), 7 pages.