(1) | |||

(2) |

where is the Lerch Transcendent. The beta function can be written in terms of the Hurwitz Zeta Function by

(3) |

(4) |

(5) |

Particular values for are

(6) | |||

(7) | |||

(8) |

where is Catalan's Constant.

**References**

Abramowitz, M. and Stegun, C. A. (Eds.).
*Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.*
New York: Dover, pp. 807-808, 1972.

Spanier, J. and Oldham, K. B. ``The Zeta Numbers and Related Functions.''
Ch. 3 in *An Atlas of Functions.* Washington, DC: Hemisphere, pp. 25-33, 1987.

© 1996-9

1999-05-24