A note on certain transformation formulas related to Appell, Horn and Kamp\'{e} de F\'{e}riet functions
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In 2019, Mathur and Solanki \cite{7,8} obtained a few transformation formulas for Appell, Horn and the Kamp\'{e} de F\'{e}riet 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.
Abstract
In 2019, Mathur and Solanki \cite{7,8} obtained a few transformation formulas for Appell, Horn and the Kamp\'{e} de F\'{e}riet 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.
참고문헌 (11)
- P. Appell, "Sur les fonctions hyp´erg´eometriques de plusieurs variables, M´emoir Sci. Math" (1925), Gauthier-Villars
- W. N. BAILEY, "ON THE SUM OF A TERMINATING <sub>2<", sub><i>F<, sub>(1), pp.The Quarterly Journal of Mathematics, 1953[DOI]
- A. Erd´elyi, "Transformations of hypergeometric functions of two variables", Proc. Roy. Soc. Edinburgh Sect. A, 62, pp.378~385 (1948)
- J. Horn, "Hypergeometrische Funktionen zweier Ver¨anderlichen", Math. Ann, 105(1), pp.381~407 (1931)[DOI]
- J. Kamp´e de F´eriet, "Les fonctions hyperg´eom´etriques d’ordre sup´erieura deux variables", CR Acad. Sci. Paris, 173, pp.401~404 (1921)
- Y. S. Kim, "Generalization of Kummer’s second theorem with applications", Comput. Math. Math. Phys, 50(3), pp.387~402 (2010)[DOI]
- R. Mathur, "Transformation formulas of Appell series F2 with contiguous extensions", J. Gujrat Research Society, 21(1), pp.336~340 (2019)
- R. Mathur, "On the transformation formulas of Appell hypergeometric function F2", J. Gujrat Research Society, 21(16), pp.2590~2596 (2019)
- E. D. Rainville, "Special Functions" (1960), The Macmillan Company
- A. K. Rathie, "On Kummer’s second theorem involving product of generalized hypergeometric series", Matematiche (Catania), 50(1), pp.35~38 (1995)
- H. M. Srivastava, "Multiple Gaussian hypergeometric series, Ellis Horwood Series: Mathematics and its Applications" (1985), Ellis Horwood Ltd.