Dirichlet beta function

In mathematics, the Dirichlet beta function is a special function, closely related to the Riemann zeta function.

Definition

The Dirichlet beta function is defined as

$\beta (s)=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)^{s}}}$

Functional equation

The functional equation is given by

$\beta (s)=...$

References

• J. Spanier and K. B. Oldham, An Atlas of Functions, (1987) Hemisphere, New York.