Whittaker Differential Equation
المؤلف:
Abramowitz, M. and Stegun, I. A
المصدر:
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover
الجزء والصفحة:
...
12-7-2018
1174
Whittaker Differential Equation
 |
(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.
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.
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