Reduction formulas for the Appell and Humbert functions

ABSTRACT Representations are obtained for some special cases of the Appell functions , and the Humbert functions in terms of elementary and simpler special functions.

[1]  Yu. A. Brychkov,et al.  On some formulas for the Appell function , 2017 .

[2]  Yu. A. Brychkov,et al.  Some properties of the Owen T-function , 2016 .

[3]  Yu. A. Brychkov,et al.  A special function of communication theory , 2015 .

[4]  George K. Karagiannidis,et al.  Analytic Expressions and Bounds for Special Functions and Applications in Communication Theory , 2014, IEEE Transactions on Information Theory.

[5]  Nasser Saad,et al.  On some formulas for the Appell function F2 (a, b, b′; c, c′; w; z) , 2014 .

[6]  Yu. A. Brychkov On some properties of the Nuttall function Qμ, ν(a, b) , 2014 .

[7]  Vladimir V. Bytev,et al.  HYPERgeometric functions DIfferential REduction (HYPERDIRE): MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: FD and FS Horn-type hypergeometric functions of three variables , 2013, Comput. Phys. Commun..

[8]  Nasser Saad,et al.  Some formulas for the Appell function F 1 (a, b, b′; c; w, z) , 2012 .

[9]  Bernd A. Kniehl,et al.  Finding new relationships between hypergeometric functions by evaluating Feynman integrals , 2011, 1108.6019.

[10]  R. Vidunas DIHEDRAL GAUSS HYPERGEOMETRIC FUNCTIONS , 2008, 0807.4888.

[11]  M. Shpot A massive Feynman integral and some reduction relations for Appell functions , 2007, 0711.2742.

[12]  Yu. A. Brychkov,et al.  Integrals and series , 1992 .

[13]  Y. Luke Inequalities for generalized hypergeometric functions of two variables , 1974 .

[14]  I︠u︡. A Brychkov Handbook of Special Functions: Derivatives, Integrals, Series and Other Formulas , 2008 .

[15]  P. Appell,et al.  Fonctions hypergéométriques et hypersphériques : polynomes d'Hermite , 1926 .