Whittaker Function

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)

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.

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