Whittaker functions
The functions and
which are solutions of the Whittaker equation
![]() | (*) |
The function satisfies the equation
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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:
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with the modified Bessel functions and the Macdonald function:
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with the probability integral:
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with the Laguerre polynomials:
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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) |
Comments
The Whittaker function can be expressed in terms of the
-function introduced in confluent hypergeometric function:
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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. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Whittaker_functions&oldid=49213