Solutions to the Whittaker Differential Equation. The linearly independent solutions are
(1) |
and , where is a Confluent Hypergeometric Function. In terms of
Confluent Hypergeometric Functions, the Whittaker functions are
(2) |
(3) |
(4) |
(5) |
(6) |
(7) |
(8) |
See also Confluent Hypergeometric Function, Kummer's Formulas, Pearson-Cunningham Function, Schlömilch's Function, Sonine Polynomial
References
Abramowitz, M. and Stegun, C. A. (Eds.). ``Confluent Hypergeometric Functions.'' Ch. 13 in
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, pp. 503-515, 1972.
Iyanaga, S. and Kawada, Y. (Eds.). ``Whittaker Functions.'' Appendix A, Table 19.II in
Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 1469-1471, 1980.
Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England:
Cambridge University Press, 1990.
© 1996-9 Eric W. Weisstein