Neville theta function: Representations through equivalent functions (formula 09.09.27.0008)

NevilleThetaC

$Mathematica Notation$

Elliptic Functions

NevilleThetaC[z,m]

Representations through equivalent functions

With related functions

Involving theta functions

http://functions.wolfram.com/09.09.27.0008.01

Input Form

NevilleThetaC[z, m] == (Sqrt[Pi]/(Sqrt[2] m^(1/4) Sqrt[EllipticK[m]])) EllipticTheta[2, (Pi z)/(2 EllipticK[m]), EllipticNomeQ[m]]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Equal]", RowBox[List[FractionBox[SqrtBox["\[Pi]"], RowBox[List[SqrtBox["2"], " ", SuperscriptBox["m", RowBox[List["1", "/", "4"]]], " ", SqrtBox[RowBox[List["EllipticK", "[", "m", "]"]]]]]], " ", RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", " ", RowBox[List["EllipticK", "[", "m", "]"]]]]], ",", RowBox[List["EllipticNomeQ", "[", "m", "]"]]]], "]"]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> ϑ </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <msqrt> <mi> π </mi> </msqrt> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mroot> <mi> m </mi> <mn> 4 </mn> </mroot> <mo> ⁢ </mo> <msqrt> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </msqrt> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <msub> <mi> ϑ </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> , </mo> <mrow> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> m </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <apply> <times /> <pi /> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> EllipticNomeQ </ci> <ci> m </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["EllipticTheta", "[", RowBox[List["2", ",", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["2", " ", RowBox[List["EllipticK", "[", "m", "]"]]]]], ",", RowBox[List["EllipticNomeQ", "[", "m", "]"]]]], "]"]]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox["m", RowBox[List["1", "/", "4"]]], " ", SqrtBox[RowBox[List["EllipticK", "[", "m", "]"]]]]]]]]]]

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

2001-10-29