Ramanujan tau theta function: Series representations (formula 10.12.06.0024)

RamanujanTauTheta

$Mathematica Notation$

Zeta Functions and Polylogarithms

RamanujanTauTheta[z]

Series representations

Generalized power series

Expansions at z==z₀/;z₀!=+-6i+-i n

http://functions.wolfram.com/10.12.06.0024.01

Input Form

RamanujanTauTheta[z] \[Proportional] RamanujanTauTheta[Subscript[z, 0]] (1 + O[z - Subscript[z, 0]]) /; Subscript[z, 0]^2 != -(6 + k)^2 && Element[k, Integers]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["RamanujanTauTheta", "[", "z", "]"]], "\[Proportional]", RowBox[List[RowBox[List["RamanujanTauTheta", "[", SubscriptBox["z", "0"], "]"]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["z", "-", SubscriptBox["z", "0"]]], "]"]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List[SubsuperscriptBox["z", "0", "2"], "\[NotEqual]", RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["6", "+", "k"]], ")"]], "2"]]]]], "\[And]", RowBox[List["k", "\[Element]", "Integers"]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> τθ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mrow> <mi> τθ </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msubsup> <mi> z </mi> <mn> 0 </mn> <mn> 2 </mn> </msubsup> <mo> ≠ </mo> <mrow> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ∧ </mo> <mrow> <mi> k </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> τθ </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <ci> τθ </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> O </ci> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <neq /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <ci> k </ci> <cn type='integer'> 6 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <in /> <ci> k </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RamanujanTauTheta", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["RamanujanTauTheta", "[", SubscriptBox["zz", "0"], "]"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]]]], ")"]]]], "/;", RowBox[List[RowBox[List[SubsuperscriptBox["zz", "0", "2"], "\[NotEqual]", RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["6", "+", "k"]], ")"]], "2"]]]]], "&&", RowBox[List["k", "\[Element]", "Integers"]]]]]]]]]]

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

2007-05-02