Year 2019,
, 1706 - 1711, 08.12.2019
Gradimir V. Milovanovic
Arjun K. Rathie
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.
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.