Dirichlet Beta Function
 |  |  | (1) |
|  |  | (2) |
where
is the Lerch Transcendent. The beta function can be written in terms of the Hurwitz ZetaFunction 
by | (3) |
as | (4) |
is an Euler Number. The beta function can be defined over the whole Complex Plane using Analytic Continuation, | (5) |
is the Gamma Function. Particular values for 
are
 | |  | (6) |
 | |  | (7) |
 | |  | (8) |
where
is Catalan's Constant.See also Catalan's Constant, Dirichlet Eta Function, Dirichlet LambdaFunction, Hurwitz Zeta Function, Lerch Transcendent, Riemann Zeta Function, Zeta Function
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.
- Halting Problem
- Hamiltonian Circuit
- Hamiltonian Cycle
- Hamiltonian Graph
- Hamiltonian Group
- Hamiltonian Map
- Hamiltonian Path
- Hamiltonian System
- Hamilton's Equations
- Hamilton's Rules
- Hammer-Aitoff Equal-Area Projection
- Hamming Function
- Ham Sandwich Theorem
- Handedness
- Handkerchief Surface
- Handle
- Handlebody
- Hankel Function
- Hankel Function of the First Kind
- Hankel Function of the Second Kind
- Hankel Matrix
- Hankel's Integral
- Hankel Transform
- Hann Function
- Hanning Function