Year 2019,
, 1706 - 1711, 08.12.2019
Gradimir V. Milovanovic
,
Arjun K. Rathie
References
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Formulas, Graphs, and Mathematical Tables, Dover, New York, 1972.
- [2] W.N. Bailey, Products of generalized hypergeometric series, Proc. Lond. Math. Soc.
s2-28 (1), 242-254, 1928.
- [3] J. Choi and A.K. Rathie, Quadratic transformations involving hypergeometric functions
of two and higher order, East Asian Math. J. 22, 71-77, 2006.
- [4] W. Chu, Telescopic approach to a formula of ${}_2F_1$-series by Gosper and Ebisu, Proc.
Japan Acad. Ser. A Math. Sci. 93 (3), 13-15, 2017.
- [5] A. Ebisu, On a strange evaluation of the hypergeometric series by Gosper, Ramanujan
J. 32 (1), 101-108, 2013.
- [6] H. Exton, Quadratic transformations involving hypergeometric functions of higher
order, Ganita 54, 13-15, 2003.
- [7] I. Gessel and D. Stanton, Strange evaluations of hypergeometric series, SIAM J. Math.
Anal. 13 (2), 295-308, 1982.
- [8] R.Wm. Gosper, Private Communication to Richard Askey, Dec. 21, 1977.
- [9] Y.S. Kim, A.K. Rathie and R.B. Paris, A note on a hypergeometric transformation
formula due to Slater with application, Math. Aeterna, 5 (1), 217-223, 2015.
- [10] G.V. Milovanović, R.K. Parmar and A.K. Rathie, A study of generalized summation
theorems for the series ${}_2F_1$ with an applications to Laplace transforms of convolution
type integrals involving Kummer’s functions ${}_1F_1$, Appl. Anal. Discrete Math. 12 (1),
257-272, 2018.
- [11] T. Pogany and A.K. Rathie, Extension of a quadratic transformation due to Exton,
Appl. Math. Comput. 215, 423-426, 2009.
- [12] M.A. Rakha and A.K. Rathie, Generalizations of classical summation theorems for
the series ${}_{2}F_{1}$ and ${}_3F_{2}$ with applications, Integral Transforms Spec. Funct. 229 (11),
823-840, 2011.
- [13] L.J. Slater, Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge,
1966.
- [14] H.M. Srivastava and H.L. Manocha, A Treatise on Generating Functions, Ellis Horwood
Ltd., Chichester, 1984.
On a quadratic transformation due to Exton and its generalization
Year 2019,
, 1706 - 1711, 08.12.2019
Gradimir V. Milovanovic
,
Arjun K. Rathie
Abstract
In 2003, Exton established numerous quadratic transformation formulas. The aim of this short note is to provide generalization of one of the quadratic transformation formulas.
References
- [1] M. Abramowitz and I.A. Stegun (Eds.) Handbook of Mathematical Functions with
Formulas, Graphs, and Mathematical Tables, Dover, New York, 1972.
- [2] W.N. Bailey, Products of generalized hypergeometric series, Proc. Lond. Math. Soc.
s2-28 (1), 242-254, 1928.
- [3] J. Choi and A.K. Rathie, Quadratic transformations involving hypergeometric functions
of two and higher order, East Asian Math. J. 22, 71-77, 2006.
- [4] W. Chu, Telescopic approach to a formula of ${}_2F_1$-series by Gosper and Ebisu, Proc.
Japan Acad. Ser. A Math. Sci. 93 (3), 13-15, 2017.
- [5] A. Ebisu, On a strange evaluation of the hypergeometric series by Gosper, Ramanujan
J. 32 (1), 101-108, 2013.
- [6] H. Exton, Quadratic transformations involving hypergeometric functions of higher
order, Ganita 54, 13-15, 2003.
- [7] I. Gessel and D. Stanton, Strange evaluations of hypergeometric series, SIAM J. Math.
Anal. 13 (2), 295-308, 1982.
- [8] R.Wm. Gosper, Private Communication to Richard Askey, Dec. 21, 1977.
- [9] Y.S. Kim, A.K. Rathie and R.B. Paris, A note on a hypergeometric transformation
formula due to Slater with application, Math. Aeterna, 5 (1), 217-223, 2015.
- [10] G.V. Milovanović, R.K. Parmar and A.K. Rathie, A study of generalized summation
theorems for the series ${}_2F_1$ with an applications to Laplace transforms of convolution
type integrals involving Kummer’s functions ${}_1F_1$, Appl. Anal. Discrete Math. 12 (1),
257-272, 2018.
- [11] T. Pogany and A.K. Rathie, Extension of a quadratic transformation due to Exton,
Appl. Math. Comput. 215, 423-426, 2009.
- [12] M.A. Rakha and A.K. Rathie, Generalizations of classical summation theorems for
the series ${}_{2}F_{1}$ and ${}_3F_{2}$ with applications, Integral Transforms Spec. Funct. 229 (11),
823-840, 2011.
- [13] L.J. Slater, Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge,
1966.
- [14] H.M. Srivastava and H.L. Manocha, A Treatise on Generating Functions, Ellis Horwood
Ltd., Chichester, 1984.