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
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Power series
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Low-order polylogarithms
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Finite sums:
- , (geometric series)
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Infinite sums, valid for (see polylogarithm):
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The following is a useful property to calculate low-integer-order polylogarithms recursively in closed form:
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Exponential function
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- (cf. mean of Poisson distribution)
- (cf. second moment of Poisson distribution)
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where is the Touchard polynomials.
Trigonometric, inverse trigonometric, hyperbolic, and inverse hyperbolic functions
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Modified-factorial denominators
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- [1]
- [1]
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Binomial coefficients
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- (see Binomial theorem)
- [2]
- [2] , generating function of the Catalan numbers
- [2] , generating function of the Central binomial coefficients
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Binomial coefficients
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- (see Multiset)
- (see Vandermonde identity)
Trigonometric functions
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Sums of sines and cosines arise in Fourier series.
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Rational functions
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- [5]
See also
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References
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