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.

© 1996-9

1999-05-26