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variants of this functions
WeierstrassSigma






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassSigma[z,{g2,g3}] > Transformations > Addition formulas > Translation by half-periods





http://functions.wolfram.com/09.15.16.0007.01









  


  










Input Form





WeierstrassSigma[i, Subscript[z, 1] + Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}] WeierstrassSigma[ Subscript[z, 1] - Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}] == WeierstrassSigma[Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}] WeierstrassSigma[i, Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}] WeierstrassSigma[j, Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}] WeierstrassSigma[k, Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}] - WeierstrassSigma[Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}] WeierstrassSigma[i, Subscript[z, 2], {Subscript[g, 2], Subscript[g, 3]}] WeierstrassSigma[j, Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}] WeierstrassSigma[k, Subscript[z, 1], {Subscript[g, 2], Subscript[g, 3]}] /; Element[{i, j, k}, {1, 2, 3}] && i != j != k










Standard Form





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MathML Form







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</ci> <ci> j </ci> </apply> <apply> <ci> CompoundExpression </ci> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> &#963; </ci> <ci> k </ci> </apply> <apply> <ci> CompoundExpression </ci> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <list> <ci> i </ci> <ci> j </ci> <ci> k </ci> </list> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 2 </cn> <cn type='integer'> 3 </cn> </list> </apply> <apply> <neq /> <ci> i </ci> <ci> j </ci> <ci> k </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List["i_", ",", RowBox[List[SubscriptBox["z_", "1"], "+", SubscriptBox["z_", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List[RowBox[List[SubscriptBox["z_", "1"], "-", SubscriptBox["z_", "2"]]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List[SubscriptBox["zz", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["i", ",", SubscriptBox["zz", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["j", ",", SubscriptBox["zz", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["k", ",", SubscriptBox["zz", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], "-", RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List[SubscriptBox["zz", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["i", ",", SubscriptBox["zz", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["j", ",", SubscriptBox["zz", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], " ", RowBox[List["WeierstrassSigma", "[", RowBox[List["k", ",", SubscriptBox["zz", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List["i", ",", "j", ",", "k"]], "}"]], "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]], "&&", RowBox[List["i", "\[NotEqual]", "j", "\[NotEqual]", "k"]]]]]]]]]]










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





2001-10-29