Catalan's constant
In mathematics, Catalan's constant G is the alternating sum of the reciprocals of the odd square numbers: G = ∑ n = 0 ∞ ( − 1 ) n ( 2 n + 1 ) 2 = 1 1 2 − 1 3 2 + 1 5 2 − 1 7 2 + 1 9 2 − ⋯ . {\displaystyle G=\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)^{2}}}={\frac {1}{1^{2}}}-{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}-{\frac {1}{7^{2}}}+{\frac {1}{9^{2}}}-\cdots .} Its numerical value is approximately (sequence A006752 in the OEIS) G = 0.915965594177219015054603514932384110774..., and it is also equal to β(2) where β is the Dirichlet beta function.