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RiemannSiegelZ






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RiemannSiegelZ[z] > Differentiation > Low-order differentiation





http://functions.wolfram.com/10.04.20.0002.01









  


  










Input Form





D[RiemannSiegelZ[z], {z, 2}] == (1/16) RiemannSiegelZ[z] (2 (PolyGamma[1, 1/4 - (I z)/2] - PolyGamma[1, 1/4 + (I z)/2]) - (PolyGamma[1/4 - (I z)/2] + PolyGamma[1/4 + (I z)/2] - 2 Log[Pi])^2 + (-((8 Derivative[1][Zeta][1/2 + I z])/Zeta[1/2 + I z])) (PolyGamma[1/4 - (I z)/2] + PolyGamma[1/4 + (I z)/2] - 2 Log[Pi]) - (16 Derivative[2][Zeta][1/2 + I z])/Zeta[1/2 + I z])










Standard Form





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MathML Form







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type='integer'> 1 </cn> <apply> <plus /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> PolyGamma </ci> <cn type='integer'> 1 </cn> <apply> <plus /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <apply> <ci> PolyGamma </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> PolyGamma </ci> <apply> 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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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