confluent hypergeometric function | Kummer's function | Kummer's function of the second kind

The confluent hypergeometric function of the first kind _1 F_1(a;b;z) is a degenerate form of the hypergeometric function _2 F_1(a, b;c;z) which arises as a solution the confluent hypergeometric differential equation. It is also known as Kummer's function of the first kind. There are a number of other notations used for the function, including F(α, β, x), M(a, b, z), Φ(a;b;z), and ∞ u(a, b, x). An alternate form of the solution to the confluent hypergeometric differential equation is known as the Whittaker function. The confluent hypergeometric function of the first kind is implemented in the Wolfram Language as Hypergeometric1F1[a, b, z].

confluent hypergeometric differential equation | confluent hypergeometric function of the second kind | confluent hypergeometric limit function | generalized hypergeometric function | hypergeometric function | hypergeometric series | Kummer's formulas | q-hypergeometric function | Weber-Sonine formula | Whittaker function