On bounds for solutions of monotonic first order difference-differential systems

Many special functions are solutions of first order linear systems y′ n(x) = an(x)yn(x) + dn(x)yn−1(x), y ′ n−1(x), = bn(x)yn−1(x) + en(x)yn(x) . We obtain bounds for the ratios yn(x)/yn-1(x) and the logarithmic derivatives of yn(x) for solutions of monotonic systems satisfying certain initial conditions. For the case dn(x)en(x) > 0, sequences of upper and… CONTINUE READING