| has gloss | eng: In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular singularity. (The term "confluent" refers to the merging of singular points of families of differential equations; "confluere" is Latin for "to flow together".) There are several common standard forms of confluent hypergeometric functions: *Kummers (confluent hypergeometric) function (for Ernst Kummer) is the family of solutions to a differential equation known as Kummers equation. There is a different but unrelated Kummers function bearing the same name. * Whittaker functions (for E. T. Whittaker) are solutions to Whittakers equation. *Coulomb wave functions are solutions to Coulomb wave equation. The Kummer functions, Whittaker functions, and Coulomb wave functions are essentially the same, and differ from each other only by elementary functions and change of variables. |