Partial Differential Approximants for Multivariable Power Series. I. Definitions and Faithfulness

M. E. Fisher, D. F. Styer
1982 Proceedings of the Royal Society A  
Fj/l(x) = [J/L]px)= ~Uj(x)/PL where Uj and PL are polynomials of degrees J and L, respectively, with coefficients Uj andpj chosen so th a t the expansion of F(x) agrees with (1.1) a t least to terms of order J + L ^ I. (The unorthodox minus sign in (1.2) is included merely for con sistency with conventions natural in the more general contexts arising below.) Pade approximants are easily computed since the + + 2 defining coefficients, Uj and pt, may be found simply by solving the set of + 1
more » ... r algebraic equations implied by the generating relation (1.3) Partial differential I 263
doi:10.1098/rspa.1982.0158 fatcat:bt4camzzrnebxcaxafboka73om