[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.
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.
[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.
Milovanovic, G. V., & Rathie, A. K. (2019). On a quadratic transformation due to Exton and its generalization. Hacettepe Journal of Mathematics and Statistics, 48(6), 1706-1711. https://doi.org/10.15672/HJMS.2019.663
AMA
Milovanovic GV, Rathie AK. On a quadratic transformation due to Exton and its generalization. Hacettepe Journal of Mathematics and Statistics. Aralık 2019;48(6):1706-1711. doi:10.15672/HJMS.2019.663
Chicago
Milovanovic, Gradimir V., ve Arjun K. Rathie. “On a Quadratic Transformation Due to Exton and Its Generalization”. Hacettepe Journal of Mathematics and Statistics 48, sy. 6 (Aralık 2019): 1706-11. https://doi.org/10.15672/HJMS.2019.663.
EndNote
Milovanovic GV, Rathie AK (01 Aralık 2019) On a quadratic transformation due to Exton and its generalization. Hacettepe Journal of Mathematics and Statistics 48 6 1706–1711.
IEEE
G. V. Milovanovic ve A. K. Rathie, “On a quadratic transformation due to Exton and its generalization”, Hacettepe Journal of Mathematics and Statistics, c. 48, sy. 6, ss. 1706–1711, 2019, doi: 10.15672/HJMS.2019.663.
ISNAD
Milovanovic, Gradimir V. - Rathie, Arjun K. “On a Quadratic Transformation Due to Exton and Its Generalization”. Hacettepe Journal of Mathematics and Statistics 48/6 (Aralık 2019), 1706-1711. https://doi.org/10.15672/HJMS.2019.663.
JAMA
Milovanovic GV, Rathie AK. On a quadratic transformation due to Exton and its generalization. Hacettepe Journal of Mathematics and Statistics. 2019;48:1706–1711.
MLA
Milovanovic, Gradimir V. ve Arjun K. Rathie. “On a Quadratic Transformation Due to Exton and Its Generalization”. Hacettepe Journal of Mathematics and Statistics, c. 48, sy. 6, 2019, ss. 1706-11, doi:10.15672/HJMS.2019.663.
Vancouver
Milovanovic GV, Rathie AK. On a quadratic transformation due to Exton and its generalization. Hacettepe Journal of Mathematics and Statistics. 2019;48(6):1706-11.