A note on two general reduction formulas for the Srivastava--Daoust double hypergeometric functions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 1, pp. 48-54.

Voir la notice de l'article provenant de la source Math-Net.Ru

The aim of this note is to provide two new and general reduction formulas for the Srivastava–Doust double hypergeometric functions. A few interesting special cases have also been given.
Keywords: hypergeometric functions, Humbert double hypergeometric functions, Appell functions, Srivastava $\&$ Daoust double hypergeometric function, beta integral method.
@article{JSFU_2024_17_1_a5,
     author = {Musharraf Ali and Harsh Vardhan Harsh and Arjun K. Rathie},
     title = {A note on two general reduction formulas for the {Srivastava--Daoust} double hypergeometric functions},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {48--54},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2024_17_1_a5/}
}
TY  - JOUR
AU  - Musharraf Ali
AU  - Harsh Vardhan Harsh
AU  - Arjun K. Rathie
TI  - A note on two general reduction formulas for the Srivastava--Daoust double hypergeometric functions
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2024
SP  - 48
EP  - 54
VL  - 17
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2024_17_1_a5/
LA  - en
ID  - JSFU_2024_17_1_a5
ER  - 
%0 Journal Article
%A Musharraf Ali
%A Harsh Vardhan Harsh
%A Arjun K. Rathie
%T A note on two general reduction formulas for the Srivastava--Daoust double hypergeometric functions
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2024
%P 48-54
%V 17
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2024_17_1_a5/
%G en
%F JSFU_2024_17_1_a5
Musharraf Ali; Harsh Vardhan Harsh; Arjun K. Rathie. A note on two general reduction formulas for the Srivastava--Daoust double hypergeometric functions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 1, pp. 48-54. http://geodesic.mathdoc.fr/item/JSFU_2024_17_1_a5/

[1] T.Appell, K. de Fériet, Fonctions Hypergeometriques et Hyperspheriques; Polynomes d'Hermite, Gauthier–Villers, Paris, 1926

[2] W.N.Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935 ; Reprinted Stechert-Hafner, New York, 1964 | MR | Zbl

[3] Yu.A.Brychkov, Handbook of Special Functions, Derivatives, Integrals, Series and Other Formulas, Chapman $\$ Hall/CRC Press, Boca Raton, 2008 | MR | Zbl

[4] Yu.A.Brychkov, Y.S.Kim, A.K.Rathie, “On a new reduction formulas for the Humbert functions $\Psi_{2}, \Phi_{2}$ and $\Phi_{3}$”, Integral Transforms Spec. Func., 28:5 (2017), 350–360 | DOI | MR | Zbl

[5] J.L.Burchnall, T.W.Chaundy, “Expansions of Appell's double hypergeometric functions”, Quart. J. Math. (Oxford ser.), 11 (1940), 249–270 | DOI | MR | Zbl

[6] J.L.Burchnall, T.W.Chaundy, “Expansions of Appell's double hypergeometric functions (II)”, Quart. J. Math. (Oxford ser.), 12 (1941), 112–128 | DOI | MR | Zbl

[7] A.Erdelyi, W.Magnus, F.Oberhettinger, F.C.Tricomi, Higher Transcendental Functions, v. I, McGraw-Hill Book Company, New York–Toronto–London, 1953 | MR

[8] I.S.Gradshteyn, I.M.Ryzhyk, Tables of Integrals, Sreies and Products, Academic Press, New York, 2007 | MR

[9] C.Krattenthaler, K.S.Rao, “Automatic generation of hypergeometric identities by the beta integral method”, J. Comput. Appl. Math., 160 (2003), 159–173 | DOI | MR | Zbl

[10] A.P.Prudnikov, Yu.A.Brychkov, O.I.Marichev, Integrals and Series, More Special Functions, v. 3, Gordon and Breach, New York, 1990 | MR | Zbl

[11] E.D.Rainville, Special Functions, Macmillan Company, New York, 1960 ; Reprinted Chelsea Publishing Company, New York, 1971 | MR | Zbl | Zbl

[12] M.A.Rakha, A.K.Rathie, “Generalizations of classical summation theorems for the series $_{2}F_{1}$ and $_{3}F_{2}$ with applications”, Integral Transforms Spec. Func., 22:11 (2011), 823–840 | DOI | MR | Zbl

[13] H.M.Srivastava, M.C.Daoust, “Certain generalized Neumann expansions associated with Kampé de Fériet functions”, Indag. Math., 31 (1969), 449–457 | MR

[14] H.M.Srivastava, M.C.Daoust, “On Eulerian integrals associated with Kampé de Fériet functions”, Publ. Inst. Math. (Beograd) (N.S.), 9 (1969), 199–202 | MR | Zbl

[15] H.M.Srivastava, M.C.Daoust, “A note on the convergence of Kampé de Fériet double hypergeometric series”, Math. Nachr., 53 (1972), 151–159 | DOI | MR | Zbl

[16] H.M.Srivastava, P.W.Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited), Chichester; John Wiley and Sons, New York–Chichester–Brisbane–Toronto, 1985 | MR | Zbl

[17] H.M. Srivastava, H.L.Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited), Chichester; John Wiley and Sons, New York–Chichester–Brisbane–Toronto, 1984 | MR | Zbl

[18] H.M.Srivastava, R.Panda, “An integral representation for the product of two Jacobi polynomials”, J. London Math. Soc., 12:2 (1976), 419–425 | DOI | MR | Zbl

[19] C.Wei,, X.Wang, Y.Li, “Certain transformations for multiple hypergeometric functions”, Adv. Diff. Equ., 360 (2013), 1–13 | DOI | MR