Sums of powers
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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
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Infinite sum (for ) |
Finite sum
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where and
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where Lis(x) is the polylogarithm of x.
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Simple denominators
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Factorial denominators
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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)
- (c.f. second moment of Poisson distribution)
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Modified-factorial denominators
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Binomial series
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Geometric series:
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Binomial Theorem:
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- with generalized binomial coefficients
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Square root:
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Miscellaneous:
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Binomial coefficients
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Trigonometric functions
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Sums of sines and cosines arise in Fourier series.
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Unclassified
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Related pages
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