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variants of this functions
Zeta






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > Zeta[s] > Series representations > Exponential Fourier series





http://functions.wolfram.com/10.01.06.0005.01









  


  










Input Form





Zeta[s] == 2 (2 Pi)^(s - 1) Gamma[1 - s] (Sin[(Pi s)/2] Sum[Cos[2 Pi k]/k^(1 - s), {k, 1, Infinity}] + Cos[(Pi s)/2] Sum[Sin[2 Pi k]/k^(1 - s), {k, 1, Infinity}]) /; Re[s] < 1










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29





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