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variants of this functions
WeierstrassSigma






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.15.20.0008.01









  


  










Input Form





D[WeierstrassSigma[z, {Subscript[g, 2], Subscript[g, 3]}], {Subscript[g, 2], 2}] == (1/(256 (Subscript[g, 2]^3 - 27 Subscript[g, 3]^2)^2)) (WeierstrassSigma[z, {Subscript[g, 2], Subscript[g, 3]}] (-24 z^2 Subscript[g, 2]^3 Subscript[g, 3] (-4 + z WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]) - 16 Subscript[g, 2]^4 (-5 + z^2 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] + 5 z WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] - z^2 WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]^2) - 216 Subscript[g, 2] Subscript[g, 3]^2 (-20 + z^2 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] + 14 z WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] - z^2 WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]^2) + 1296 Subscript[g, 3]^2 (z^2 Subscript[g, 3] - 3 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^2 - 4 WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] - 6 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]^2 + WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]^4) + 9 Subscript[g, 2]^2 Subscript[g, 3] (z^4 Subscript[g, 3] + 32 (z WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] + WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]^2 (6 - z WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]) + 3 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] (-2 + z WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}])))))










Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2001-10-29





© 1998- Wolfram Research, Inc.