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.

Sums of powers

See also triangle number. This is one of the most useful series: many applications can be found throughout mathematics.

Where  is the th Bernoulli number,  is negative and  is the binomial coefficient (choose function).

Where  is the Riemann zeta function.

Power series
 Infinite sum (for )   Finite sum where  and    where Lis(x) is the polylogarithm of x.


Simple denominators

Factorial denominators
Many power series which arise from Taylor's theorem have a coefficient containing a factorial.

 (c.f. mean of Poisson distribution)
 (c.f. second moment of Poisson distribution)

Modified-factorial denominators

 Binomial series 
Geometric series:

Binomial Theorem:

with generalized binomial coefficients


Square root:

Miscellaneous:
 Theoretical computer science cheat sheet 




 Binomial coefficients 

 Trigonometric functions 
Sums of sines and cosines arise in Fourier series.

 Unclassified 

Related pages
 Series (mathematics)
 List of integrals
 Summation
 Taylor series
 Binomial theorem
 Gregory's series

Notes

References
Many books with a list of integrals also have a list of series.

Category:Mathematics lists
Category:Sequences and series