confluent hypergeometric function | Tricomi function

The confluent hypergeometric function of the second kind gives the second linearly independent solution to the confluent hypergeometric differential equation. It is also known as the Kummer's function of the second kind, Tricomi function, or Gordon function. It is denoted U(a, b, z) and can be defined by U(a, b, z) | = | π csc(π b)[(_1 F^~_1(a;b;z))/(Γ(a - b + 1)) - (z^(1 - b) _1 F^~_1(a - b + 1;2 - b;z))/(Γ(a))] | = | z^(-a) _2 F_0(a, 1 + a - b;; - z^(-1)),

Bateman function | confluent hypergeometric function of the first kind | confluent hypergeometric limit function | Coulomb wave function | Cunningham function | Gordon function | hypergeometric function | Poisson-Charlier polynomial | Toronto function | Weber functions | Whittaker function