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)),
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