Linear equations with elements (l/m)k(n/m) + δ_nm and infinitely many variables

Extract

Introduction. Infinite systems

are discussed in which k(θ) and b(n) are differentiable. The aim is to determine the behaviour of a(n) for large n and to reduce (1) to a finite system. This involves solving

for the high order a(n), n ≥ N, in terms of the preceding a(n), with a large enough N to facilitate the iteration procedure employed. The desired N − 1, N − 1 system follows on substitution for the high order a(n) in the first N − 1 equations (1).