On some formulas for the generalized Appell type functions
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
A remarkably large number of special functions (such as the Gamma and Beta functions, the Gauss hypergeometric function, and so on) have been investigated by many authors. Motivated the works of both works of both Burchnall and Chaundy and Chaundy and very recently, Brychkov and Saad gave interesting generalizations of Appell type functions. In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present some new differential formulas for the generalized Appell's type functions $\kappa _{i},i=1,2,\ldots,18$ by considering the product of two $_{4}F_{3}$ functions.
Abstract
A remarkably large number of special functions (such as the Gamma and Beta functions, the Gauss hypergeometric function, and so on) have been investigated by many authors. Motivated the works of both works of both Burchnall and Chaundy and Chaundy and very recently, Brychkov and Saad gave interesting generalizations of Appell type functions. In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present some new differential formulas for the generalized Appell's type functions $\kappa _{i},i=1,2,\ldots,18$ by considering the product of two $_{4}F_{3}$ functions.
참고문헌 (24)
- P. Agarwal, "Certain integrals involving the generalized hypergeometric function and the Laguerre polynomials", J. Comput. Appl. Math, 313, pp.307~317 (2017)
- P. Agarwal, "On the extended Appell-Lauricella hyperge-ometric functions and their applications", Filomat
- Praveen Agarwal, "Certain integrals involving ${}_2F_1$, Kamp\'{e} De F\'{e}riet function and Srivastava polynomials", 대한수학회논문집, 31(2), pp.343~353 (2016), 대한수학회
- Praveen Agarwal, "Extended hypergeometric functions of two and three variables", 대한수학회논문집, 30(4), pp.403~414 (2015), 대한수학회
- P. Appell, "Sur une classe de polyn^omes", Ann. Sci. ^E cole Norm. Sup. (2), 9, pp.119~144 (1880)
- W. N. Baily, "Generalized Hypergeometric Series" (1935)
- Yu. A. Brychkov, "Handbook of Special Functions" (2008), CRC Press, Taylor & Fancis Group
- Yu. A. Brychkov, "On some formulas for the Appell function F1(a; b; b0;c;w; z)", Integral Transforms Spec. Funct, 23(11), pp.793~802 (2012)
- Yu. A. Brychkov, "On some formulas for the Appell function F2(a; b; b0; c; c0;w; z)", Integral Transforms Spec. Funct, 25(2), pp.111~123 (2014)
- J. L. Burchnall, "Expansions of Appell's double hypergeometric functions", Quart. J. Math. Oxford Ser, 11, pp.249~270 (1940)
- J. L. Burchnall, "Expansions of Appell's double hypergeometric functions (II)", Quart. J. Math. Oxford Ser, 12, pp.112~128 (1941)
- T. W. Chaundy, "Expansions of hypergeometric functions", Quart. J. Math. Oxford Ser, 13, pp.159~171 (1942)
- J. Choi, "Applications of the operator H( ; ) to the Humbert double hypergeometric functions", Comput. Math. Appl, 61(3), pp.663~671 (2011)
- J. Choi, "Certain generalized Appell type functions and their properties", Appl. Math. Sci, 9, pp.6567~6581 (2015)
- S. Jain, "Generating functions for the generalized Appell func-tion", Int. J. Math. Anal, 10(1), pp.1~7 (2016)
- M. A. Khan, "On a generalizations of Appell's functions of two variables", Pro Math, 16(31-32), pp.61~83 (2002)
- G. Lauricella, "Sulle funzioni ipergeometriche a pi ù variabili", Rend. Circ. Mat. Palermo, 7, pp.111~158 (1893)
- E. D. Rainville, "Special Functions" (1971), Chelsea Publishing Company
- L. Saalschütz, "Zeits", für Math. Soc, 25, pp.114~132 (1907)
- M. Saigo, "A Remark on integral operators involving hypergeometric functions", Math. Rep. Kuyshu Univ, 11(2), pp.135~143 (1978)
- H. M. Srivastava, "Certain double integrals involving hypergeometric functions", Jnanbha Sect. A, 1(1), pp.1~10 (1971)
- H. M. Srivastava, "Zeta and q-Zeta Functions and Associated Series and Integrals" (2012), Elsevier Science Publishers
- H. M. Srivastava, "Multiple Gaussian Hypergeometric Series" (1985), Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons
- H. M. Srivastava, "A Treatise on Generating Functions" (1984), Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons