대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제38권3호
  • /
  • Pages.807-819
  • /
  • 2023
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

A NOTE ON CERTAIN TRANSFORMATION FORMULAS RELATED TO APPELL, HORN AND KAMPÉ DE FÉRIET FUNCTIONS

  • Asmaa Orabi Mohammed (Department of Mathematics Faculty of Science Suez Canal University) ;
  • Medhat Ahmed Rakha (Department of Mathematics Faculty of Science Suez Canal University) ;
  • Arjun K. Rathie (Department of Mathematics Vedant College of Engineering & Technology Rajasthan Technical University)
  • 투고 : 2022.07.20
  • 심사 : 2022.11.15
  • 발행 : 2023.07.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In 2019, Mathur and Solanki [7, 8] obtained a few transformation formulas for Appell, Horn and the Kampé de Fériet functions. Unfortunately, some of the results are well-known and very old results in literature while others are erroneous. Thus the aim of this note is to provide the results in corrected forms and some of the results have been written in more compact form.

키워드

과제정보

The authors are grateful to the learned referee for making certain useful suggestions which led to better presentation of the paper.

참고문헌

  1. P. Appell, Sur les fonctions hypergeometriques de plusieurs variables, Memoir Sci. Math., Gauthier-Villars, Paris, 1925.
  2. W. N. Bailey, On the sum of a terminating 3F2(1), Quart. J. Math. Oxford Ser. (2) 4 (1953), 237-240. https://doi.org/10.1093/qmath/4.1.237
  3. A. Erdelyi, Transformations of hypergeometric functions of two variables, Proc. Roy. Soc. Edinburgh Sect. A 62 (1948), 378-385.
  4. J. Horn, Hypergeometrische Funktionen zweier Veranderlichen, Math. Ann. 105 (1931), no. 1, 381-407. https://doi.org/10.1007/BF01455825
  5. J. Kampe de Feriet, Les fonctions hypergeometriques d'ordre superieura deux variables, CR Acad. Sci. Paris 173 (1921), 401-404.
  6. Y. S. Kim, M. A. Rakha, and A. K. Rathie, Generalization of Kummer's second theorem with applications, Comput. Math. Math. Phys. 50 (2010), no. 3, 387-402; translated from Zh. Vychisl. Mat. Mat. Fiz. 50 (2010), no. 3, 407-422. https://doi.org/10.1134/S0965542510030024
  7. R. Mathur and N. S. Solanki, Transformation formulas of Appell series F2 with contiguous extensions, J. Gujrat Research Society 21 (2019), no. 1, 336-340.
  8. R. Mathur and N. S. Solanki, On the transformation formulas of Appell hypergeometric function F2, J. Gujrat Research Society 21 (2019), no. 16, 2590-2596.
  9. E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960.
  10. A. K. Rathie and V. Nagar, On Kummer's second theorem involving product of generalized hypergeometric series, Matematiche (Catania) 50 (1995), no. 1, 35-38.
  11. H. M. Srivastava and P. W. Karlsson, Multiple Gaussian hypergeometric series, Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester, 1985.