The term "confluence" has distinct uses in mathematics. For a reduction system, confluence is the property that two reduction paths from the same element can be continued to a common result. A reduction system with this property is confluent.
In the theory of differential equations, confluence is a limiting process in which singular points coalesce. The confluent hypergeometric differential equation arises as a limiting form of the hypergeometric differential equation in which two regular singular points coalesce into an irregular singularity. Its solutions include the confluent hypergeometric functions of the first and second kinds.
