Confluent hypergeometric function

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: