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WeierstrassZeta






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.17.20.0006.01









  


  










Input Form





D[WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}], {Subscript[g, 2], 2}] == (1/(16 (Subscript[g, 2]^3 - 27 Subscript[g, 3]^2)^2)) (162 z Subscript[g, 3]^3 + Subscript[g, 2]^4 (z WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] - z^2 WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] - 3 WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]) + 36 Subscript[g, 2]^2 Subscript[g, 3] (2 z WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^2 - 4 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] + WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] (-2 + z WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}])) + 27 Subscript[g, 3]^2 (Subscript[g, 2] (7 z WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] - WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]) - 12 (WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] + 4 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^2 WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] + WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]^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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