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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.

Details

Primary Language English
Subjects Mathematics
Journal Section Mathematics
Authors

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

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

Cite

Bibtex @research article { hujms534982, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, pages = {1706 - 1711}, doi = {10.15672/HJMS.2019.663}, title = {On a quadratic transformation due to Exton and its generalization}, key = {cite}, author = {Milovanovic, Gradimir V. and Rathie, Arjun K.} }
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 . DOI: 10.15672/HJMS.2019.663
MLA Milovanovic, G. V. , Rathie, A. K. "On a quadratic transformation due to Exton and its generalization" . Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1706-1711 <https://dergipark.org.tr/en/pub/hujms/article/534982>
Chicago Milovanovic, G. V. , Rathie, A. K. "On a quadratic transformation due to Exton and its generalization". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1706-1711
RIS TY - JOUR T1 - On a quadratic transformation due to Exton and its generalization AU - Gradimir V. Milovanovic , Arjun K. Rathie Y1 - 2019 PY - 2019 N1 - doi: 10.15672/HJMS.2019.663 DO - 10.15672/HJMS.2019.663 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1706 EP - 1711 VL - 48 IS - 6 SN - 2651-477X-2651-477X M3 - doi: 10.15672/HJMS.2019.663 UR - https://doi.org/10.15672/HJMS.2019.663 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics On a quadratic transformation due to Exton and its generalization %A Gradimir V. Milovanovic , Arjun K. Rathie %T On a quadratic transformation due to Exton and its generalization %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 6 %R doi: 10.15672/HJMS.2019.663 %U 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 (December 2019): 1706-1711 . https://doi.org/10.15672/HJMS.2019.663
AMA Milovanovic G. V. , Rathie A. K. On a quadratic transformation due to Exton and its generalization. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1706-1711.
Vancouver Milovanovic G. V. , Rathie A. K. On a quadratic transformation due to Exton and its generalization. Hacettepe Journal of Mathematics and Statistics. 2019; 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, Dec. 2019, doi:10.15672/HJMS.2019.663