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WeierstrassInvariants






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassInvariants[{w1,w3}] > Differentiation > Fractional integro-differentiation > With respect to omega1





http://functions.wolfram.com/09.19.20.0009.01









  


  










Input Form





D[WeierstrassInvariants[{Subscript[\[Omega], 1], Subscript[\[Omega], 3]}], {Subscript[\[Omega], 1], \[Alpha]}] == {(Pi^4/12) FDPowerConstant[Subscript[\[Omega], 1], -4, \[Alpha]] Subscript[\[Omega], 1]^(-4 - \[Alpha]) + (15/(Subscript[\[Omega], 1]^\[Alpha] (2 Subscript[\[Omega], 3]^4))) Sum[(1/n^4) Hypergeometric2F1Regularized[1, 4, 1 - \[Alpha], -((m Subscript[\[Omega], 1])/(n Subscript[\[Omega], 3]))], {m, -Infinity, Infinity}, {n, 1, Infinity}], (Pi^6/216) FDPowerConstant[Subscript[\[Omega], 1], -6, \[Alpha]] Subscript[\[Omega], 1]^(-6 - \[Alpha]) + (35/(Subscript[\[Omega], 1]^\[Alpha] (8 Subscript[\[Omega], 3]^6))) Sum[(1/n^6) Hypergeometric2F1Regularized[1, 6, 1 - \[Alpha], -((m Subscript[\[Omega], 1])/(n Subscript[\[Omega], 3]))], {m, -Infinity, Infinity}, {n, 1, 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





© 1998- Wolfram Research, Inc.