linear form;
Mahler function;
Hermite-Pade approximation;
GENERATING-FUNCTIONS;
CONTINUED FRACTIONS;
SEQUENCE;
NUMBERS;
APPROXIMATIONS;
D O I:
10.1017/S0308210518000148
中图分类号:
O29 [应用数学];
学科分类号:
070104 ;
摘要:
We estimate the linear independence measures for the values of a class of Mahler functions of degrees 1 and 2. For this purpose, we study the determinants of suitable Hermite-Pade approximation polynomials. Based on the non-vanishing property of these determinants, we apply the functional equations to get an infinite sequence of approximations that is used to produce the linear independence measures.