Research Article
Year 2019, Volume 48, Issue 6, 1706 - 1711, 08.12.2019

### 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, Volume 48, Issue 6, 1706 - 1711, 08.12.2019

### 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.

### Details

Primary Language English Mathematics Mathematics Gradimir V. MİLOVANOVİC (Primary Author) University of Niš 0000-0002-3255-8127 Serbia Arjun K. RATHİE This is me Vedant College of Engineering and Technology 0000-0003-3902-3050 India December 8, 2019 Year 2019, Volume 48, Issue 6