Catalan's constant

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Catalan's constant $\scriptstyle K\,$ (or $\scriptstyle G\,$), named after Eugène Charles Catalan, is defined as

$K:=\beta (2)=\sum _{i=0}^{\infty }{\frac {(-1)^{i}}{(2i+1)^{2}}},\,$

where $\scriptstyle \beta (s)\,$ is the Dirichlet beta function.

It is not known whether $\scriptstyle K\,$ is irrational, let alone transcendental.

Decimal expansion of Catalan's constant

The decimal expansion of Catalan's constant is

$K=$ 0.915965594177219015054603514932384110774149374281672134266498... (A006752)

Continued fraction

The simple continued fraction for Catalan's constant gives the sequence of integer part and partial quotients (A014538)

{0, 1, 10, 1, 8, 1, 88, 4, 1, 1, 7, 22, 1, 2, 3, 26, 1, 11, 1, 10, 1, 9, 3, 1, 1, 1, 1, 1, 1, 2, 2, 1, 11, 1, 1, 1, 6, 1, 12, 1, 4, 7, 1, 1, 2, 5, 1, 5, 9, 1, 1, 1, 1, 33, 4, 1, 1, ...}

External links

• Weisstein, Eric W., Catalan's Constant, from MathWorld—A Wolfram Web Resource. [http://mathworld.wolfram.com/CatalansConstant.html]