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Yadav, Vijay
- Elliptic WP-Bailey Transform and its Applications
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Authors
Affiliations
1 Department of Mathematics, T.D.P.G. College, Jaunpur-222002 (UP), IN
2 Department of Mathematics, S.P.D.T. College, Andheri (E), Mumbai-400059, IN
1 Department of Mathematics, T.D.P.G. College, Jaunpur-222002 (UP), IN
2 Department of Mathematics, S.P.D.T. College, Andheri (E), Mumbai-400059, IN
Source
The Journal of the Indian Mathematical Society, Vol 86, No 1-2 (2019), Pagination: 179-186Abstract
In this paper, idea of WP-Bailey transform has been extended to elliptic WP-Bailey transform and it has been applied to establish certain interesting summation and transformation formulas for elliptic and theta hypergeometric series.Keywords
Elliptic Hypergeometric Series, Theta Hypergeometric Series, Wp-Bailey Transform, Elliptic Wp-Bailey Transform, Summation Formula, Transformation Formula.
References
- G. Gasper and M. Rahman, Basic hypergeometric series (Second Edition), Cambridge University Press, New York, 2004.
- H. M. Srivastava, S. N. Singh, Satya Prakash Singh, Vijay Yadav, Certain Derived WP-Bailey Pairs and Transformation Formulas for q-Hypergeometric Series, Filomat, 31(14) (2017), pp. 4619-4628.
- H. M. Srivastava, S. N. Singh, Satya Prakash Singh, Vijay Yadav, Some conjugate WP-Bailey pairs and transformation formulas for q-series, CREAT. MATH. INFORM, 24(2) (2015), pp. 199-209.
- Satya Prakash Singh, On transformation formulae for theta hypergeometric functions, J. Ramanujan Society of Math. and Math. Sc., 3(1) (2014), pp.53-62.
- Satya Prakash Singh, On a transformation formula for elliptic hypergeometric series, South East Asian J. Math.& Math. Sc., 10(2) (2011), pp. 79-87.
- S. N. Singh, Satya Prakash Singh, Vijay Yadav, On Bailey’s Transform and Expansion of Basic Hypergeometric Functions-II, South East Asian J. of Math.& Math. Sci., 11(2), (2015), pp. 37-46.
- S. O. Warnaar, Extensions of the well-poised and elliptic well poised Bailey lemma, Indag Math. (N.S.) to appear at XIV. Math: CA/0309241.
- V. P. Spiridonov, An elleptic extension of the Bailey chain, Int. Math. Res. Notices, 37 (2002), pp. 1945-1977.
- On Certain Basic Hypergeometric Series Identities
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Authors
Affiliations
1 Department of Mathematics, TDPG College, Jaunpur-222002, IN
2 Department of Mathematics, SPDT College, Andheri (E), Mumbai, IN
1 Department of Mathematics, TDPG College, Jaunpur-222002, IN
2 Department of Mathematics, SPDT College, Andheri (E), Mumbai, IN
Source
The Journal of the Indian Mathematical Society, Vol 90, No 3-4 (2023), Pagination: 367–374Abstract
In this paper, making use of an identity, certain Rogers-Ramanujan type identities have been established.Keywords
q-Series, Identity, Continued Fraction.References
- G. E. Andrews and B. C. Berndt, Ramanujan’s Lost Notebook, Part I, Springer, Berlin, New York, 2005.
- G. E. Andrews and B. C. Berndt, Ramanujan’s Lost Notebook, Part II, Springer, Berlin, New York, 2009.
- G. E. Andrews and B. C. Berndt, Ramanujan’s Lost Notebook, Part V, Springer, Berlin, New York, 2018.
- G. E. Andrews, R. A. Askey, B. C. Berndt, K. G. Ramanathan and R. A. Rankin, Ramanujan Revisited, Proceedings of the Centenary Conference, University of Illinois at Urbana Champaign, June 1-5, 1987, Academic Press, INC., Harcourt Brace Jovanovich, Publishers, Boston San Diego, New York, Berkaley, London, Sydney, Tokyo, Toronto, 1987.
- S. Bhargava and C. Adiga, A basic bilateral series summation formula and its applications, Integral transforms and Special functions, 2(3) (1994), 165–184.
- Harold Exton, q-Hypergeometric Functions and Applications, Ellis Horwood Limited, Halsted Press: a division of John Willey & Sons, New York, 1983.
- G. Gasper and M. Rahman, Basic Hypergeometric Series (Second Edition), Cambridge University Press, New York, 2004.
- A. Verma, On Identities of Rogers-Ramanujan type, Indian J. Pure and Appl. Math., 11 (6) (1980), 770–790.