Some explicit formulae in simultaneous padé approximation

AbstractUsing old results on the explicit calculation of determinants, formulae are given for the coefficients of P0(z) and P0(z)fi(z) − Pi(z), where Pi(z) are polynomials of degree σ − ρi (i=0,1,…,n), P0(z)fi(z) − Pi(z) are power series in which the terms with zk, 0⩽k⩽σ, vanish (i=1,2,…,n), (ρ0,ρ1,…,ρn) is an (n+1)-tuple of nonnegative integers, σ=ρ0+ρ1+⋯+ρn, and {fi}ni=1 is the set of hypergeometric functions {1F1(1;ci;z)}ni=1 (ci∉Zz.drule;N, ci − cj∉Z) or {2F0(ai,1;z)}ni=1 (ai ∉Z⧹N, ai − aj∉Z) under the condition ρ0⩾ρi − 1 (i=1,2,…,n)