List of mathematical series

This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums.

See Faulhaber's formula.

The first few values are:

See zeta constants.

The first few values are:

Finite sums:

Infinite sums, valid for ${\displaystyle |z|<1}$ (see polylogarithm):

The following is a useful property to calculate low-integer-order polylogarithms recursively in closed form:

where ${\displaystyle T_{n}(z)}$ is the Touchard polynomials.

Sums of sines and cosines arise in Fourier series.

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