[1] Appell P, Kampé de Fériet J. Fonctions Hypergéométriques et Hypersphériques Polynomes D'Hermite. Paris: Gauthier-Villars, 1926 [2] Bailey W N. Generalized Hypergeometric Series, Cambridge Tracts in Mathematics and Mathematical Physics 32. London: Cambridge University Press, 1935 [3] Bezrodnykh S I.Analytic continuation of Lauricella's function $ F_D^{(N)} $ for large in modulo variables near hyperplanes $ \{z_j=z_l\} $. Integral Transforms Spec Funct, 2022, 33(4): 276-291 [4] Bezrodnykh S I.Analytic continuation of Lauricella's function $ F_D^{(N)} $ for variables close to unit near hyperplanes $ \{z_j=z_l\} $. Integral Transforms Spec Funct, 2022, 33(5): 419-433 [5] Bezrodnykh S I.Analytic continuation of the Kampé de Fériet function and the general double Horn series. Integral Transforms Spec Funct, 2022, 33(11): 908-928 [6] Buschman R G, Srivastava H M.Series identities and reducibility of Kampé de Fériet functions. Math Proc Cambridge Philos Soc, 1982, 91(3): 435-440 [7] Bytev V V, Kniehl B A.Derivatives of any Horn-type hypergeometric functions with respect to their parameters. Nuclear Phys B, 2020, 952: 114911 [8] Carlitz L.Summation of a special $ _4F_3 $. Boll Unione Mat Ital, 1963, 18: 90-93 [9] Chan W C C, Chen K Y, Chyan C J, Srivastava H M. Some multiple hypergeometric transformations and associated reduction formulas. J Math Anal Appl, 2004, 294(2): 418-437 [10] Chen K Y, Srivastava H M.Series identities and associated families of generating functions. J Math Anal Appl, 2005, 311(2): 582-599 [11] Chu W C, Li N N.Reduction and summation formulae for semi-terminating $ q $-Kampé de Fériet series. Afrika Matematika, 2013, 24(4): 647-664 [12] Chu W C, Srivastava H M.Ordinary and basic bivariate hypergeometric transformations associated with the Appell and Kampé de Fériet functions. J Comput Appl Math, 2003, 156(2): 355-370 [13] Chu W C, Zhang W L.Well-posed reduction formulas for the $ q $-Kampé de Fériet function. Ukrainian Math J, 2011, 62(11): 1783-1802 [14] Cvijović D, Miller A R.A reduction formula for the Kampé de Fériet function. Appl Math Lett, 2010, 23(7): 769-771 [15] Gasper G.Positive integrals of Bessel functions. SIAM J Math Anal, 1975, 6(5): 868-881 [16] Jia C Z, Wang T M.Reduction and transformation formulae for bivariate basic hypergeometric series. J Math Anal Appl, 2007, 328(2): 1152-1160 [17] Jia C Z, Wang T M.Transformation and reduction formulae for double $ q $-Clausen series of type $ \Phi_{1:1;\mu}^{1:2;\lambda} $. J Math Anal Appl, 2007, 328(1): 609-624 [18] Kampé de Fériet J. Les fonctions hypergéométriques d'ordre supérieur à deux variables. CR Acad Sci Paris, 1921, 173: 401-404 [19] Karlsson P W.Some reducible generalized Kampé de Fériet functions. J Math Anal Appl, 1983, 96(2): 546-550 [20] Karlsson P W.Some reduction formulae for double power series and Kampé de Fériet functions. Indag Math, 1984, 87(1): 31-36 [21] Li N N, Chu W.Terminating balanced $ _4F_3 $-series and very well-poised $ _7F_6 $-series. Ramanujan J, 2019, 49: 465-482 [22] Liu H M.Hypergeometric series summations and $ \pi $-formulas. J Math Anal Appl, 2014, 419(1): 553-561 [23] Liu H M, Wang W P.Transformation and summation formulae for Kampé de Fériet series. J Math Anal Appl, 2014, 409(1): 100-110 [24] 刘红梅, 周文书, 李阳. 双变量超几何级数的变换与简化公式. 数学物理学报, 2016, 36A(1): 150-156 Liu H M, Zhou W S, Li Y.Transformation and reduction formulae for bivariate hypergeometric series. Acta Math Sci, 2016, 36A(1): 150-156 [25] Luo M J, Raina R K.On certain results related to the hypergeometric function $ F_K $. J Math Anal Appl, 2021, 504(2): 125439 [26] Mouayn Z, Chhaiba H, Kassogue H, Kikodio P K.Husimi Q-functions attached to hyperbolic Landau levels. Rep Math Phys, 2022, 89(1): 27-57 [27] Pitre S N, Van der Jeugt J. Transformation and summation formulas for Kampé de Fériet series $ F_{1:1}^{0:3}(1,1) $. J Math Anal Appl, 1996, 202(1): 121-132 [28] Santander J L G. A note on some reduction formulas for the generalized hypergeometric function $ _2F_2 $ and Kampé de Fériet function. Results Math, 2017, 71: 949-954 [29] Slater L J. Generalized Hypergeometric Functions.Cambridge: Cambridge Univ Press, 1966 [30] Rao K S, Van der Jeugt J. Stretched 9-$ j $ coefficients and summation theorems. J Phys A: Math Gen, 1994, 27(9): 3083-3090 [31] Srivastava H M, Daoust M C.A note on the convergence of Kampé de Fériet's double hypergeometric series. Math Nachr, 1972, 53(1/6): 151-159 [32] Srivastava H M, Karlsson P W.Multiple Gaussian Hypergeometric Series. Chichester: Ellis Horwood, 1985 [33] Srivastava H M, Panda R.An integral representation for the product of two Jacobi polynomials. J Lond Math Soc, 1976, 2(4): 419-425 [34] Van der Jeugt J. Transformation formula for a double Clausenian hypergeometric series, its $ q $-analogue, and its invariance group. J Comput Appl Math, 2002, 139(1): 65-73 [35] Van der Jeugt J, Pitre S N, Rao K S. Transformation and summation formulas for double hypergeometric series. J Comput Appl Math, 1997, 83(2): 185-193 [36] Zhang W L.New transformation and reduction formulae for double $ q $-Clausen series. J Math Anal Appl, 2013, 402(2): 710-718 |