Low-order polylogarithms
Finite sums:
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• $${\displaystyle \sum _{n=a+1}^{\infty }{\frac {a}{n^{2}-a^{2}}}={\frac {1}{2}}H_{2a}}$$
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These numeric series can be found by plugging in numbers from the series listed above.
Alternating harmonic series
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Sum of reciprocal … See more

1. ^ Weisstein, Eric W. "Haversine". MathWorld. Wolfram Research, Inc. Archived from the original on 2005-03-10. Retrieved 2015-11-06.
2. ^ Wilf, Herbert R. (1994). generatingfunctionology (PDF). Academic Press, Inc. See more

Sums of sines and cosines arise in Fourier series.
• $${\displaystyle \sum _{k=1}^{\infty }{\frac {\cos(k\theta )}{k}}=-{\frac {1}{2}}\ln(2-2\cos \theta )=-\ln \left(2\sin {\frac {\theta }{2}}\right),0<\theta <2\pi }$$
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• $${\displaystyle \displaystyle {\dfrac {1}{\sqrt {p}}}\sum _{n=0}^{p-1}\exp \left({\frac {2\pi in^{2}q}{p}}\right)={\dfrac {e^{\pi i/4}}{\sqrt {2q}}}\sum _{n=0}^{2q-1}\exp \left(-{\frac {\pi in^{2}p}{2q}}\right)}$$(see the Landsberg–Schaar … See more

• Series (mathematics)
• List of integrals
• Summation § Identities
• Taylor series
• Binomial theorem See more