Confluent hypergeometric function Kummer

As discussed in [45], the solution of problem (26) is then obtained in terms of the confluent hypergeometric function, also known as Kummer function iFi[a b z], readily available in the Mathematica system [41], as ... 

This is Kummer s differential equation whose regular solution at the origin is the confluent hypergeometric function lFl(—a + 1, 2, p). 

As has been known since the early studies of a spherically confined hydrogen atom [2,3]/ the required solution of Equation (10) is a confluent hypergeometric function, or Kummer M function,... 

The following equation is satisfied by the confluent hypergeometric function of Kummer... 

For continuous computation, the erf (x) can be given an asymptotic expansion (Abramowitz and Stegun 1965) or it can be represented in terms of the Confluent Hypergeometric function after Kummer (e.g., see Example 3.4). A rational approximation given by C. Hastings in Abramowitz and Stegun (1965) is useful for digital computation... 

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