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.

• Here, ${\displaystyle 0^{0}}$ is taken to have the value ${\displaystyle 1}$
• ${\displaystyle \{x\}}$ denotes the fractional part of ${\displaystyle x}$
• ${\displaystyle B_{n}(x)}$ is a Bernoulli polynomial.
• ${\displaystyle B_{n}}$ is a Bernoulli number, and here, ${\displaystyle B_{1}=-{\frac {1}{2}}.}$
• ${\displaystyle E_{n}}$ is an Euler number.
• ${\displaystyle \zeta (s)}$ is the Riemann zeta function.
• ${\displaystyle \Gamma (z)}$ is the gamma function.
• ${\displaystyle \psi _{n}(z)}$ is a polygamma function.
• ${\displaystyle \operatorname {Li} _{s}(z)}$ is a polylogarithm.
• ${\displaystyle n \choose k}$ is binomial coefficient
• ${\displaystyle \exp(x)}$ denotes exponential of ${\displaystyle x}$