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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2014 / Cilt: 43 - Sayı: 1

ON A REDUCTION FORMULA FOR THE KAMP´ E de F´ ERIET FUNCTION

Yong Sup KİM
Tibor K. POGANY
Arjun K. RATHİE
Sayfa
65–68
Yayın Tarihi
2022-10-18
DOI
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Notes 10(2), 145-153, 2009.]

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Amaç & Hipotez:The aim of this short research note is to provide a reduction formulafor the Kamp´e de F´eriet function Fh:2;0[-x, x] by employing a newg:2;0 summation formula for Clausen's series3F2[1] obtained recently by theauthors [Miskolc Math.
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Temel Bulgular & Veri:The aim of this short research note is to provide a reduction formulafor the Kamp´e de F´eriet function Fh:2;0[-x, x] by employing a newg:2;0 summation formula for Clausen's series3F2[1] obtained recently by theauthors [Miskolc Math.
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Sonuç & Katkı:Notes 10(2), 145-153, 2009.]
🔬Tür:Araştırma Makalesi
📍Kapsam:2009 Verileri
⚙️Değişkenler:Alan Parametreleri

Abstract

The aim of this short research note is to provide a reduction formulafor the Kamp´e de F´eriet function Fh:2;0[-x, x] by employing a newg:2;0 summation formula for Clausen's series3F2[1] obtained recently by theauthors [Miskolc Math. Notes 10(2), 145-153, 2009.]

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Bu Makaleye Atıf Yap

KİM, Y. S., POGANY, T. K., RATHİE, A. K. (2022). ON A REDUCTION FORMULA FOR THE KAMP´ E de F´ ERIET FUNCTION. Hacettepe Journal of Mathematics and Statistics, Cilt: 43 - Sayı: 1, 65–68. https://ajindex.com/articles/530353

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Kaynakça (14)

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  2. Bailey, W.N. Generalized Hypergeometric Series, Cambridge Tract, No. 32. (Cambridge University Press, Cambridge, 1935)
  3. Burchnall, J.L. and Chaundy, T.W. Expansions of Appell's double hypergeometric functions, Quart. J. Math. (Oxford Ser.) 11, 249-270, 1940
  4. Buschmann R.G. and Srivastava, H.M. Some identities and reducibility of Kamp´e de F´eriet function, Math. Proc. Cambridge Philos. Soc. 91, 435-440, 1982
  5. Exton, H. On the reducibility of Kamp´e de F´eriet functions, J. Comput. Appl. Math. 83, 119-121, 1997
  6. Exton H. and Krupnikov, E.D. A register of computer-oriented reduction identities for the Kamp´e de F´eriet function. Draft manuscript. (Novosibirsk, Russia, 1998)
  7. Karlsson, P.W. Some reduction formulae for power series and Kamp´e de F´eriet functions, Nederl. Akad. Wetensch. Indag. Math. 46(1), 31-36, 1984
  8. Kim,Y.-S., Pog´any, T.K. and Rathie, A.K. On a summation formula for the Clausen's series 3F2 with applications, Miskolc Math. Notes 10(2), 145-153, 2009
  9. Paris, R.B. A Kummer-type transformation for a 2F2 hypergeometric function, J. Comput. Appl. Math. 173, 379-382, 2005
  10. Rathie, A.K. and Paris, R.B. An extension of the Euler-type transformation for the 3F2 series, Far East J. Math. Sci.(FJMS) 27(1), 43-48, 2007
  11. Slater, L.J. Generalized Hypergeometric Functions, (Cambridge University Press, Cambridge, 1966)
  12. Srivastava H.M. and Karlsson, P.W. Multiple Gaussian Hypergeometric Series, (Halsted Press (Ellis Norwood Limited, Chichester), John Wiley & Sons, New York, 1985)
  13. Srivastava, H.M. and Manocha, H.L. A Treatise on Generating Functions, (Halsted Press (Ellis Norwood Limited, Chichester), John Wiley & Sons, New York, 1984)
  14. Srivastava, H.M. and Panda, R. An integral representation for the product of two Jacobi polynomials, J. London Math. Soc. (2) 12, 419-425, 1976.