Dergiler / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 6

On a quadratic transformation due to Exton and its generalization

Sayfa
1706–1711
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The aim of this short note is to provide generalization of one of the quadratic transformation formulas.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In 2003, Exton established numerous quadratic transformation formulas.
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Temel Bulgular & Veri:In 2003, Exton established numerous quadratic transformation formulas.
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Sonuç & Katkı:The aim of this short note is to provide generalization of one of the quadratic transformation formulas.
🔬Tür:Araştırma Makalesi
📍Kapsam:2003 Verileri
⚙️Değişkenler:Quadratic transformation · Bailey’s transform · Kummer’s summation theorem

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.

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Bu Makaleye Atıf Yap

Milovanović, G. V., Rathie, A. K. (2022). On a quadratic transformation due to Exton and its generalization. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 6, 1706–1711. https://ajindex.com/articles/530530

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Kaynakça (14)

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  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.