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LerchPhi






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > LerchPhi[z,s,a] > Series representations > Generalized power series > Expansions at s==s0 > For Phi^(z,s,a)





http://functions.wolfram.com/10.06.06.0033.01









  


  










Input Form





LerchPhiClassical[z, s, a] \[Proportional] LerchPhiClassical[z, Subscript[s, 0], a] (1 + O[s - Subscript[s, 0]])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", "s", ",", "a"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", SubscriptBox["s", "0"], ",", "a"]], "]"]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["s", "-", SubscriptBox["s", "0"]]], "]"]]]], ")"]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mtext> </mtext> <mrow> <mrow> <mover> <mi> &#934; </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox[&quot;z&quot;, Rule[Editable, True]] </annotation> </semantics> <mo> , </mo> <semantics> <mi> s </mi> <annotation encoding='Mathematica'> TagBox[&quot;s&quot;, Rule[Editable, True]] </annotation> </semantics> <mo> , </mo> <semantics> <mi> a </mi> <annotation encoding='Mathematica'> TagBox[&quot;a&quot;, Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mrow> <mover> <mi> &#934; </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox[&quot;z&quot;, Rule[Editable, True]] </annotation> </semantics> <mo> , </mo> <semantics> <msub> <mi> s </mi> <mn> 0 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[&quot;s&quot;, &quot;0&quot;], Rule[Editable, True]] </annotation> </semantics> <mo> , </mo> <semantics> <mi> a </mi> <annotation encoding='Mathematica'> TagBox[&quot;a&quot;, Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> s </mi> <mo> - </mo> <msub> <mi> s </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <apply> <ci> OverHat </ci> <ci> &#934; </ci> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <ci> z </ci> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <ci> s </ci> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <ci> a </ci> </apply> </apply> <apply> <times /> <apply> <apply> <ci> OverHat </ci> <ci> &#934; </ci> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <ci> z </ci> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> s </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <ci> a </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> O </ci> <apply> <plus /> <ci> s </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> s </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LerchPhiClassical", "[", RowBox[List["z_", ",", "s_", ",", "a_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["LerchPhiClassical", "[", RowBox[List["z", ",", SubscriptBox["ss", "0"], ",", "a"]], "]"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["s", "-", SubscriptBox["ss", "0"]]], "]"]]]], ")"]]]]]]]]










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





2007-05-02