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variants of this functions
WeierstrassSigma




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassSigma[z,{g2,g3}] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/09.15.20.0012.01









  


  








Input Form





D[WeierstrassSigma[z, {Subscript[g, 2], Subscript[g, 3]}], {z, \[Alpha]}] == 2^(\[Alpha] - 1) Sqrt[Pi] z^(1 - \[Alpha]) Product[1/(1 - q^(2 n)), {n, 1, Infinity}]^3 Sum[(-1)^(j + k) q^(k (1 + k)) (2 k + 1)^(2 j + 1) ((Pi z)/(4 Subscript[\[Omega], 1]))^(2 j) HypergeometricPFQRegularized[ {1 + j, 3/2 + j}, {1 + j - \[Alpha]/2, (3 - \[Alpha])/2 + j}, (z^2/(2 Subscript[\[Omega], 1])) WeierstrassZeta[Subscript[\[Omega], 1], {Subscript[g, 2], Subscript[g, 3]}]], {k, 0, Infinity}, {j, 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