Öz
The aim of this short research note is to provide a reduction formulafor the Kamp´e de F´eriet function Fh:2;0 g:2;0 [−x, x] by employing a newsummation formula for Clausen’s seriesF [1] obtained recently by theauthors [Miskolc Math. Notes 10(2), 145–153, 2009.]
Anahtar Kelimeler
Clausen’s seriesF Euler’s transformation forF Kamp´e de F´erietfunction Kummer–type I transformation forF summation formula.
Kaynakça
- Appell, P. and Kamp´ e de F´ eriet, J. Fonctions hyperg´ eom´ etrique. Polynˆ omes d’Hermite, (Gautier–Villars, Paris, 1926).
- Bailey, W.N. Generalized Hypergeometric Series, Cambridge Tract, No. 32. (Cambridge University Press, Cambridge, 1935).
- Burchnall, J.L. and Chaundy, T.W. Expansions of Appell’s double hypergeometric functions, Quart. J. Math. (Oxford Ser.) 11, 249–270, 1940.
- 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.
- Exton, H. On the reducibility of Kamp´ e de F´ eriet functions, J. Comput. Appl. Math. 83, 119–121, 1997.
- 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).
- 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.
- Kim,Y.–S., Pog´ any, T.K. and Rathie, A.K. On a summation formula for the Clausen’s series 3 F 2 with applications, Miskolc Math. Notes 10(2), 145–153, 2009.
- Paris, R.B. A Kummer–type transformation for a 2 F 2 hypergeometric function, J. Comput. Appl. Math. 173, 379–382, 2005.
- Rathie, A.K. and Paris, R.B. An extension of the Euler–type transformation for the 3 F 2 series, Far East J. Math. Sci.(FJMS) 27(1), 43–48, 2007.
- Slater, L.J. Generalized Hypergeometric Functions, (Cambridge University Press, Cambridge, 1966).
- Srivastava H.M. and Karlsson, P.W. Multiple Gaussian Hypergeometric Series, (Halsted Press (Ellis Norwood Limited, Chichester), John Wiley & Sons, New York, 1985). Srivastava, H.M. and Manocha, H.L. A Treatise on Generating Functions, (Halsted Press (Ellis Norwood Limited, Chichester), John Wiley & Sons, New York, 1984).
- 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.
Öz
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Anahtar Kelimeler
Kaynakça
- Appell, P. and Kamp´ e de F´ eriet, J. Fonctions hyperg´ eom´ etrique. Polynˆ omes d’Hermite, (Gautier–Villars, Paris, 1926).
- Bailey, W.N. Generalized Hypergeometric Series, Cambridge Tract, No. 32. (Cambridge University Press, Cambridge, 1935).
- Burchnall, J.L. and Chaundy, T.W. Expansions of Appell’s double hypergeometric functions, Quart. J. Math. (Oxford Ser.) 11, 249–270, 1940.
- 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.
- Exton, H. On the reducibility of Kamp´ e de F´ eriet functions, J. Comput. Appl. Math. 83, 119–121, 1997.
- 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).
- 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.
- Kim,Y.–S., Pog´ any, T.K. and Rathie, A.K. On a summation formula for the Clausen’s series 3 F 2 with applications, Miskolc Math. Notes 10(2), 145–153, 2009.
- Paris, R.B. A Kummer–type transformation for a 2 F 2 hypergeometric function, J. Comput. Appl. Math. 173, 379–382, 2005.
- Rathie, A.K. and Paris, R.B. An extension of the Euler–type transformation for the 3 F 2 series, Far East J. Math. Sci.(FJMS) 27(1), 43–48, 2007.
- Slater, L.J. Generalized Hypergeometric Functions, (Cambridge University Press, Cambridge, 1966).
- Srivastava H.M. and Karlsson, P.W. Multiple Gaussian Hypergeometric Series, (Halsted Press (Ellis Norwood Limited, Chichester), John Wiley & Sons, New York, 1985). Srivastava, H.M. and Manocha, H.L. A Treatise on Generating Functions, (Halsted Press (Ellis Norwood Limited, Chichester), John Wiley & Sons, New York, 1984).
- 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.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Ocak 2014 |
| Yayımlandığı Sayı | Yıl 2014 Cilt: 43 Sayı: 1 |