论文信息 - On an Integral Identity

On an Integral Identity

Abstract We give three elementary proofs of a nice equality of definite integrals, recently proven by Ekhad, Zeilberger, and Zudilin. The equality arises in the theory of bivariate hypergeometric functions, and has connections with irrationality proofs in number theory. We furthermore provide a generalization together with an equally elementary proof and discuss some consequences.

[1] K. Alladi,et al. Legendre polynomials and irrationality. , 1980 .

[2] É. Picard. Sur une extension aux fonctions de deux variables du problème de Riemann relatif aux fonctions hypergéométriques , 1881 .

[3] W. Rheinboldt,et al. Generalized hypergeometric functions , 1968 .

[4] S. Lang. Complex Analysis , 1977 .

[5] P. Appell. Sur les fonctions hypergéométriques de plusieurs variables les polynomes d'hermite et autres fonctions sphériques dans l'hyperespace , 1925 .

[6] Doron Zeilberger,et al. The Method of Differentiating under the Integral Sign , 1990, J. Symb. Comput..

[7] Leon M. Hall,et al. Special Functions , 1998 .