List of series

Wikimedia list article

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 change

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    See also triangle number. This is one of the most useful series: many applications can be found throughout mathematics.
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    Where   is the  th Bernoulli number,   is negative and   is the binomial coefficient (choose function).
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Where   is the Riemann zeta function.

Power series change

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

Simple denominators change

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Factorial denominators change

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

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  •   (c.f. mean of Poisson distribution)
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Modified-factorial denominators change

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Binomial series change

Geometric series:

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Binomial Theorem:

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with generalized binomial coefficients
 

Square root:

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Miscellaneous:

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Binomial coefficients change

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Trigonometric functions change

Sums of sines and cosines arise in Fourier series.

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Unclassified change

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Related pages change

Notes change

  1. 1.0 1.1 1.2 1.3 Theoretical computer science cheat sheet

References change