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WeierstrassZeta






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassZeta[z,{g2,g3}] > Integral representations > On the real axis > Of the direct function





http://functions.wolfram.com/09.17.07.0001.01









  


  










Input Form





WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] == 1/z - (1/4) Integrate[ ((t z - 2 Sin[t (z/2)]) E^(I t (Subscript[\[Omega], 2]/2)) Cos[t (Subscript[\[Omega], 2]/2)])/ (Sin[t ((Subscript[\[Omega], 1] - Subscript[\[Omega], 2])/2)] Sin[t ((Subscript[\[Omega], 1] + Subscript[\[Omega], 2])/2)]) - (t z - 2 Sinh[(t z)/2]) ((Cosh[t Subscript[\[Omega], 2]] + Sinh[t (Subscript[\[Omega], 2]/2)]/E^(t (Subscript[\[Omega], 2]/2)))/ (Sinh[t ((Subscript[\[Omega], 1] - Subscript[\[Omega], 2])/2)] Sinh[t ((Subscript[\[Omega], 1] + Subscript[\[Omega], 2])/2)])), {t, 0, Infinity}]










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