(1)
Let ,
where
denotes a Whittaker function . Then (1 )
becomes
(2)
Rearranging,
(3)
(4)
so
(5)
where
(Abramowitz and Stegun 1972, p. 505; Zwillinger 1997, p. 128). The solutions
are known as Whittaker functions . Replacing
by ,
the solutions can also be written in the form
(6)
where
is a confluent hypergeometric
function of the second kind and is a generalized Laguerre
polynomial .
See also Whittaker Function
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References Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, p. 505, 1972. Zwillinger, D. Handbook
of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 128,
1997. Referenced on Wolfram|Alpha Whittaker Differential Equation
Cite this as:
Weisstein, Eric W. "Whittaker Differential Equation." From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/WhittakerDifferentialEquation.html
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