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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/10.03.07.0002.01









  


  








Input Form





RiemannSiegelTheta[z] == (1/2) (Integrate[(2 Sin[(t z)/2] E^(t/4))/(t (1 - E^t)) + z/(E^t t), {t, 0, Infinity}] + I Log[Sin[Pi (1/4 + (I z)/2)]] - I Log[Sin[Pi (1/4 - (I z)/2)]]) - (Log[Pi]/2) z /; Abs[Im[z]] < 3/2








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