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WeierstrassP




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassP[z,{g2,g3}] > Representations through equivalent functions > With related functions > Involving other Weierstrass functions





http://functions.wolfram.com/09.13.27.0008.01









  


  








Input Form





(WeierstrassPPrime[Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}] - WeierstrassPPrime[Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}])/ (WeierstrassP[Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}] - WeierstrassP[Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}]) == 2 (WeierstrassZeta[Subscript[z, 1] + Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}] - WeierstrassZeta[Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}] - WeierstrassZeta[Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["z", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "-", RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["z", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], ")"]], "/", " ", RowBox[List["(", RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["z", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "-", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["z", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], ")"]]]], "\[Equal]", RowBox[List["2", RowBox[List["(", RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List[SubscriptBox["z", "1"], "+", SubscriptBox["z", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "-", RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["z", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "-", RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["z", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], ")"]]]]]]]]








MathML Form







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</mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[TagBox[RowBox[List[SubscriptBox[&quot;z&quot;, &quot;1&quot;], &quot;+&quot;, SubscriptBox[&quot;z&quot;, &quot;2&quot;]]], Rule[Editable, True]], &quot;;&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], Rule[Editable, True]]]], &quot;,&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> <mo> - </mo> <semantics> <mrow> <mi> &#950; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[RowBox[List[RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["z_", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "-", RowBox[List["WeierstrassPPrime", "[", RowBox[List[SubscriptBox["z_", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["z_", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "-", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["z_", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]]], "]"]], "\[RuleDelayed]", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List[RowBox[List[SubscriptBox["zz", "1"], "+", SubscriptBox["zz", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "-", RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["zz", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], "-", RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["zz", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], ")"]]]]]]]]


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





2001-10-29