The Confluent hypergeometric function is a special function that arises in various areas of mathematics and physics, particularly in the context of solving differential equations. It is a limit case of the more general hypergeometric function and is particularly useful in situations where the parameters of the hypergeometric function simplify, leading to the confluent form.
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Confluent hypergeometric functions solve the Kummer differential equation . The regular solution is the confluent hypergeometric function of the first kind; a second standard solution is conventionally denoted . The family arises by coalescing singular points of the Gauss hypergeometric equation.