# Catalan constant

Named after its inventor, E.Ch. Catalan (1814–1894), the Catalan constant (which is denoted also by ) is defined by (a1) If, in terms of the Digamma (or Psi) function , defined by (a2)

or one puts (a3) where then (a4)

which provides a relationship between the Catalan constant and the Digamma function .

The Catalan constant is related also to other functions, such as the Clausen function , defined by (a5) and the Hurwitz zeta function , which is defined, when , by (a6) Thus, (a7) Since (a8) the last expression in (a7) would follow also from (a4) in light of the definition in (a3).

A fairly large number of integrals and series can be evaluated in terms of the Catalan constant . For example, (a9)  (a10) and (a11)

where denotes the familiar Riemann zeta-function.

How to Cite This Entry:
Catalan constant. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Catalan_constant&oldid=38979
This article was adapted from an original article by Hari M. Srivastava (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article