List of mathematical series

• Here, is taken to have the value
• is a Bernoulli polynomial.
• is a Bernoulli number, and here,
• is an Euler number.
• is the Riemann zeta function.
• is the gamma function.
• is a polygamma function.
• is a polylogarithm.
• is binomial coefficient
• denotes exponential of

  Sums of powers

• Power series

Low-order polylogarithms

• ,

Exponential function

Trigonometric, inverse trigonometric, hyperbolic, and inverse hyperbolic functions

• Modified-factorial denominators

Binomial coefficients

• , generating function of the Catalan numbers
• , generating function of the Central binomial coefficients

• Harmonic numbers

Binomial coefficients

• Trigonometric functions

• ,

  Rational functions

• An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.

  Exponential function