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variants of this functions
Zeta






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > Zeta[s] > Identities > Functional identities > Including derivatives of the function





http://functions.wolfram.com/10.01.17.0002.01









  


  










Input Form





Derivative[n][Zeta][1 - s] == (-1)^n Sum[Binomial[n, k] (E^(s (-((I Pi)/2) - Log[2 Pi])) (-((I Pi)/2) - Log[2 Pi])^(n - k) + E^(s (-Log[2 Pi] + (I Pi)/2)) ((I Pi)/2 - Log[2 Pi])^(n - k)) D[Gamma[s] Zeta[s], {s, k}], {k, 1, Infinity}] /; Element[n, Integers] && n >= 0










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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