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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/10.03.07.0007.01









  


  










Input Form





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










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





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