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Year 2019, Volume: 48 Issue: 6, 1706 - 1711, 08.12.2019
https://doi.org/10.15672/HJMS.2019.663

Abstract

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
https://doi.org/10.15672/HJMS.2019.663

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.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Gradimir V. Milovanovic 0000-0002-3255-8127

Arjun K. Rathie This is me 0000-0003-3902-3050

Publication Date December 8, 2019
Published in Issue Year 2019 Volume: 48 Issue: 6

Cite

APA 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. December 2019;48(6):1706-1711. doi:10.15672/HJMS.2019.663
Chicago Milovanovic, Gradimir V., and Arjun K. Rathie. “On a Quadratic Transformation Due to Exton and Its Generalization”. Hacettepe Journal of Mathematics and Statistics 48, no. 6 (December 2019): 1706-11. https://doi.org/10.15672/HJMS.2019.663.
EndNote Milovanovic GV, Rathie AK (December 1, 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 and A. K. Rathie, “On a quadratic transformation due to Exton and its generalization”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 6, pp. 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 (December2019), 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. and Arjun K. Rathie. “On a Quadratic Transformation Due to Exton and Its Generalization”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 6, 2019, pp. 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.