|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/10.06.06.0004.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
LerchPhiClassical[z, s, a] \[Proportional] a^(-s) + z/(1 + a)^s +
z^2/(2 + a)^s + \[Ellipsis] /; (z -> 0)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", "s", ",", "a"]], "]"]], "\[Proportional]", RowBox[List[SuperscriptBox["a", RowBox[List["-", "s"]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], RowBox[List["-", "s"]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["2", "+", "a"]], ")"]], RowBox[List["-", "s"]]], " ", SuperscriptBox["z", "2"]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mrow> <mover> <mi> Φ </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> s </mi> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[OverscriptBox["\[CapitalPhi]", "^"], "(", RowBox[List[TagBox["z", Rule[Editable, True]], ",", TagBox["s", Rule[Editable, True]], ",", TagBox["a", Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[List[$CellContext`a, $CellContext`b, $CellContext`c], LerchPhi[$CellContext`a, $CellContext`b, $CellContext`c]]]] </annotation> </semantics> <mo> ∝ </mo> <mrow> <msup> <mi> a </mi> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mo> … </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> LerchPhi </ci> <ci> z </ci> <ci> s </ci> <ci> a </ci> </apply> <apply> <plus /> <apply> <power /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> … </ci> </apply> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LerchPhiClassical", "[", RowBox[List["z_", ",", "s_", ",", "a_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["a", RowBox[List["-", "s"]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], RowBox[List["-", "s"]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["2", "+", "a"]], ")"]], RowBox[List["-", "s"]]], " ", SuperscriptBox["z", "2"]]], "+", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|