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http://functions.wolfram.com/01.22.26.0007.01
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Coth[z] == (Sqrt[z^2]/z) Sqrt[2/3]
Sqrt[1 - WeierstrassP[I Sqrt[2/3] z, {3, 1}]] /;
!IntervalMemberQ[I z, Interval[{-(Pi/2), Pi/2}]]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Coth", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[" ", SqrtBox[SuperscriptBox["z", "2"]], " "]], "z"], SqrtBox[FractionBox["2", "3"]], SqrtBox[RowBox[List["1", "-", RowBox[List["WeierstrassP", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", SqrtBox[FractionBox["2", "3"]], " ", "z"]], ",", RowBox[List["{", RowBox[List["3", ",", "1"]], "}"]]]], "]"]]]]]]]]], "/;", "\[InvisibleSpace]", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], ",", RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], ",", FractionBox["\[Pi]", "2"]]], "}"]], "]"]]]], "]"]], "]"]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> coth </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <msqrt> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </msqrt> <mtext> </mtext> </mrow> <mi> z </mi> </mfrac> <mo> ⁢ </mo> <msqrt> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> ℘ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msqrt> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ; </mo> <mn> 3 </mn> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> </mrow> </mrow> <mo> /; </mo> <mtext> ​ </mtext> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ∉ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <mi> coth </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <msqrt> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </msqrt> <mtext> </mtext> </mrow> <mi> z </mi> </mfrac> <mo> ⁢ </mo> <msqrt> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> ℘ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msqrt> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ; </mo> <mn> 3 </mn> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> </mrow> </mrow> <mo> /; </mo> <mtext> ​ </mtext> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ∉ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SqrtBox[SuperscriptBox["z", "2"]], " ", SqrtBox[FractionBox["2", "3"]], " ", SqrtBox[RowBox[List["1", "-", RowBox[List["WeierstrassP", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", SqrtBox[FractionBox["2", "3"]], " ", "z"]], ",", RowBox[List["{", RowBox[List["3", ",", "1"]], "}"]]]], "]"]]]]]]], "z"], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], ",", RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], ",", FractionBox["\[Pi]", "2"]]], "}"]], "]"]]]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
