Polynomial type Padé approximants

Abstract

Some results are established giving conditions on f ( x ) f(x) so that its main diagonal Padé approximation R n ( x ) {R_n}(x) is of the form P n ( x ) / P n ( − x ) {P_n}(x)/{P_n}( - x) , where P n ( x ) {P_n}(x) is a polynomial in x of degree n. A number of applications to special functions are presented. Numerical computations are given for the gamma function using the "bignum" arithmetical facilities of formula manipulation languages REDUCE2, FORMAC.