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WeierstrassP






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.13.20.0008.01









  


  










Input Form





D[WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}], {Subscript[g, 3], 2}] == (-(1/(8 (Subscript[g, 2]^3 - 27 Subscript[g, 3]^2)^2))) (3 (54 Subscript[g, 3]^2 (8 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] - 6 z^2 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^2 + z WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}]) + 2 Subscript[g, 2]^3 (28 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] + 5 z WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] + 6 WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]^2) - 12 Subscript[g, 2]^2 (16 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^3 - WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}]^2 + 12 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] + 12 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^2 WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]^2 + Subscript[g, 3] (-10 + 3 z WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}])) + 27 Subscript[g, 2] Subscript[g, 3] (z^2 Subscript[g, 3] + 8 (z WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] - WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] + 2 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^2 (-1 + z WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}])))))










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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