Hypergeometric, supertrigonometric, and superhyperbolic functions via Clausen hypergeometric series
暂无分享,去创建一个
[1] Eric T. Mortenson. Supercongruences for truncated n+1Fn hypergeometric series with applications to certain weight three newforms , 2004 .
[2] C. Lennon. Trace formulas for Hecke operators, Gaussian hypergeometric functions, and the modularity of a threefold , 2011 .
[3] K. Ono,et al. Gaussian hypergeometric functions and traces of Hecke operators , 2004 .
[4] F. J. W. Whipple. A Fundamental Relation between Generalized Hypergeometric Series , 1926 .
[5] Dennis Stanton,et al. A character sum evaluation and Gaussian hypergeometric series , 1986 .
[6] A. Plastino,et al. From the hypergeometric differential equation to a non-linear Schrödinger one , 2015, 1505.01334.
[7] T. Koornwinder. Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators , 2015, 1504.08144.
[8] N. Sonine,et al. Recherches sur les fonctions cylindriques et le développement des fonctions continues en séries , 1880 .
[9] Dennis Stanton,et al. Bijective proofs of basic hypergeometric series identities , 1987 .
[10] Hari M. Srivastava,et al. Some reduction and transformation formulas for the Appell hypergeometric function F2 , 2005 .
[11] Distributional solutions of the hypergeometric differential equation , 1987 .
[12] P. W. Karlsson. Clausen′s Hypergeometric Series with Variable 1/4 , 1995 .
[13] George E. Andrews,et al. Applications of Basic Hypergeometric Functions , 1974 .
[14] K. Takemura. Heun's equation, generalized hypergeometric function and exceptional Jacobi polynomial , 2011, 1106.1543.
[15] Yu-Ming Chu,et al. Asymptotical formulas for Gaussian and generalized hypergeometric functions , 2016, Appl. Math. Comput..
[16] Carsten Schneider,et al. Gaussian Hypergeometric series and supercongruences , 2006, Math. Comput..
[17] A. W. Kemp,et al. A treatise on generating functions , 1984 .
[18] Jacques Dutka. The early history of the hypergeometric function , 1984 .
[19] K. Ono. Values of Gaussian hypergeometric series , 1998 .
[20] Gustavo Gasaneo,et al. Derivatives of any order of the Gaussian hypergeometric function 2F1(a, b, c; z) with respect to the parameters a, b and c , 2009 .
[21] W. N. Bailey. Products of Generalized Hypergeometric Series , 1928 .
[22] R. Paris,et al. Clausen's series 3 F 2(1) with integral parameter differences and transformations of the hypergeometric function 2 F 2(x) , 2012 .
[23] Edwards Curves and Gaussian Hypergeometric Series , 2015, 1501.03526.
[24] H. Bateman,et al. An Orthogonal Property of the Hypergeometric Polynomial. , 1942, Proceedings of the National Academy of Sciences of the United States of America.
[25] Ranjan Roy,et al. Binomial identities and hypergeometric series , 1986 .
[26] Spectral properties of solutions of hypergeometric-type differential equations , 1994 .
[27] B. Dwork. On Kummer’s twenty-four solutions of the hypergeometric differential equation , 1984 .
[28] Eric T. Mortenson. Supercongruences between truncated 2F1 hypergeometric functions and their Gaussian analogs , 2002 .
[29] Th. Clausen,et al. Ueber die Fälle, wenn die Reihe von der Form y = etc. ein Quadrat von der Form z = etc. hat. , 1828 .
[30] N. E. Nørlund. Hypergeometric functions , 1955 .
[31] E. W. Barnes. A New Development of the Theory of the Hypergeometric Functions , 1908 .