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variants of this functions
InverseWeierstrassP






Mathematica Notation

Traditional Notation









Elliptic Functions > InverseWeierstrassP[z,{g2,g3}] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/09.22.06.0003.01









  


  










Input Form





InverseWeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] \[Proportional] InverseWeierstrassP[Subscript[z, 0], {Subscript[g, 2], Subscript[g, 3]}] + (z - Subscript[z, 0])/Sqrt[-Subscript[g, 3] - Subscript[g, 2] Subscript[z, 0] + 4 Subscript[z, 0]^3] - ((12 z^2 - Subscript[g, 2])/ (4 (-Subscript[g, 3] - Subscript[g, 2] Subscript[z, 0] + 4 Subscript[z, 0]^3)^(3/2))) (z - Subscript[z, 0])^2 + ((Subscript[g, 2]^2 - 8 z Subscript[g, 2] (6 z - 5 Subscript[z, 0]) + 16 z (15 z^3 + Subscript[g, 3] - 10 Subscript[z, 0]^3))/ (8 (-Subscript[g, 3] - Subscript[g, 2] Subscript[z, 0] + 4 Subscript[z, 0]^3)^(5/2))) (z - Subscript[z, 0])^3 - (1/(64 (-Subscript[g, 3] - Subscript[g, 2] Subscript[z, 0] + 4 Subscript[z, 0]^3)^(7/2))) (-5 Subscript[g, 2]^3 - 16 Subscript[g, 2] (525 z^4 + 12 z Subscript[g, 3] - 7 (60 z^3 + Subscript[g, 3]) Subscript[z, 0] - 168 z Subscript[z, 0]^3 + 70 Subscript[z, 0]^4) + 32 (840 z^6 + 60 z^3 Subscript[g, 3] + Subscript[g, 3]^2 - 14 (60 z^3 + Subscript[g, 3]) Subscript[z, 0]^3 + 70 Subscript[z, 0]^6) + 4 Subscript[g, 2]^2 (150 z^2 + 7 Subscript[z, 0] (-24 z + 5 Subscript[z, 0]))) (z - Subscript[z, 0])^4 + (1/(640 (-Subscript[g, 3] - Subscript[g, 2] Subscript[z, 0] + 4 Subscript[z, 0]^3)^(9/2))) (35 Subscript[g, 2]^4 + 96 Subscript[g, 2]^2 (25 z (98 z^3 + Subscript[g, 3]) - 18 (175 z^3 + Subscript[g, 3]) Subscript[z, 0] + 945 z^2 Subscript[z, 0]^2 - 450 z Subscript[z, 0]^3 + 252 Subscript[z, 0]^4) + 11520 z^2 (385 z^6 + 28 z^3 Subscript[g, 3] + Subscript[g, 3]^2 - 18 (28 z^3 + Subscript[g, 3]) Subscript[z, 0]^3 + 126 Subscript[z, 0]^6) - 384 Subscript[g, 2] (4900 z^6 + 175 z^3 Subscript[g, 3] + Subscript[g, 3]^2 - 135 z^2 (28 z^3 + Subscript[g, 3]) Subscript[z, 0] - 18 (175 z^3 + Subscript[g, 3]) Subscript[z, 0]^3 + 1890 z^2 Subscript[z, 0]^4 + 126 Subscript[z, 0]^6) - 48 Subscript[g, 2]^3 (175 z^2 + 9 Subscript[z, 0] (-25 z + 7 Subscript[z, 0]))) (z - Subscript[z, 0])^5 + \[Ellipsis] /; (z -> Subscript[z, 0])










Standard Form





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MathML Form







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</mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 640 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msubsup> <mi> z </mi> <mn> 0 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> - </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 35 </mn> <mo> &#8290; </mo> <msubsup> <mi> g </mi> <mn> 2 </mn> <mn> 4 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 48 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 175 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <msub> <mi> z </mi> <mn> 0 </mn> 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Rule Form





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





2007-05-02





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