# Whittaker functions

The functions and which are solutions of the Whittaker equation

 (*)

The function satisfies the equation

The pairs of functions and are linearly independent solutions of the equation (*). The point is a branching point for , and is an essential singularity.

Relation with other functions:

with the degenerate hypergeometric function:

with the modified Bessel functions and the Macdonald function:

with the probability integral:

with the Laguerre polynomials:

#### References

 [1] H. Bateman (ed.) A. Erdélyi (ed.) et al. (ed.) , Higher transcendental functions , 2. Bessel functions, parabolic cylinder functions, orthogonal polynomials , McGraw-Hill (1953) [2] E.T. Whittaker, G.N. Watson, "A course of modern analysis" , Cambridge Univ. Press (1952)