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 probability integral:
with the Laguerre polynomials:
|||H. Bateman (ed.) A. Erdélyi (ed.) et al. (ed.) , Higher transcendental functions , 2. Bessel functions, parabolic cylinder functions, orthogonal polynomials , McGraw-Hill (1953)|
|||E.T. Whittaker, G.N. Watson, "A course of modern analysis" , Cambridge Univ. Press (1952)|
The Whittaker function can be expressed in terms of the -function introduced in confluent hypergeometric function:
Thus, the special cases discussed in confluent hypergeometric function can be rewritten as special cases for the Whittaker functions. See also the references given there.
Whittaker functions. Yu.A. BrychkovA.P. Prudnikov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Whittaker_functions&oldid=12501