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WeierstrassPPrime






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.14.20.0007.01









  


  










Input Form





D[WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}], {Subscript[g, 3], 2}] == (1/(8 (Subscript[g, 2]^3 - 27 Subscript[g, 3]^2)^2)) (3 (5 z Subscript[g, 2]^4 + 162 Subscript[g, 3]^2 (2 z WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^2 - 3 WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] + 4 z^2 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}]) - 6 Subscript[g, 2]^3 (10 z WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^2 + 9 WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] + 20 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]) + 36 Subscript[g, 2]^2 (8 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^2 WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] + Subscript[g, 3] (5 z WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] - 4 WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]) + 24 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^3 WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] + 2 WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}]^2 WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] + 8 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}]^2) + 27 Subscript[g, 2] Subscript[g, 3] (3 z Subscript[g, 3] - 4 (12 z WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^3 + z WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}]^2 - 8 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}]^2 WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}] + 4 WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] WeierstrassPPrime[z, {Subscript[g, 2], Subscript[g, 3]}] (-1 + 2 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





© 1998-2014 Wolfram Research, Inc.