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RiemannSiegelTheta






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RiemannSiegelTheta[z] > Integral representations > On the real axis > Of the direct function





http://functions.wolfram.com/10.03.07.0008.01









  


  










Input Form





RiemannSiegelTheta[z] == (-(1/2)) z Log[Pi] - (I/2) Integrate[(1/t) ((I z)/E^t - ((1 + t)^(-(1/4) - (I z)/2) ((1 + t)^(I z) - 1))/Log[1 + t]), {t, 0, Infinity}] /; Im[z] == 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