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variants of this functions
Zeta






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > Zeta[s,a] > Series representations > Generalized power series > Expansions at a==a0/;a0!=-n > For zeta(s,a)





http://functions.wolfram.com/10.02.06.0033.01









  


  










Input Form





Zeta[s, a] \[Proportional] (Zeta[s, Subscript[a, 0]] - Zeta[s, 1 + Floor[-Re[Subscript[a, 0]]] + Subscript[a, 0]] + Zeta[s, Max[0, 1 + Floor[-Re[Subscript[a, 0]]]] + Subscript[a, 0]]) (1 + O[a - Subscript[a, 0]])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Zeta", "[", RowBox[List["s", ",", "a"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Zeta", "[", RowBox[List["s", ",", SubscriptBox["a", "0"]]], "]"]], "-", RowBox[List["Zeta", "[", RowBox[List["s", ",", RowBox[List["1", "+", RowBox[List["Floor", "[", RowBox[List["-", RowBox[List["Re", "[", SubscriptBox["a", "0"], "]"]]]], "]"]], "+", SubscriptBox["a", "0"]]]]], "]"]], "+", RowBox[List["Zeta", "[", RowBox[List["s", ",", RowBox[List[RowBox[List["Max", "[", RowBox[List["0", ",", RowBox[List["1", "+", RowBox[List["Floor", "[", RowBox[List["-", RowBox[List["Re", "[", SubscriptBox["a", "0"], "]"]]]], "]"]]]]]], "]"]], "+", SubscriptBox["a", "0"]]]]], "]"]]]], ")"]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["a", "-", SubscriptBox["a", "0"]]], "]"]]]], ")"]]]]]]]]










MathML Form







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</mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> s </mi> <mo> , </mo> <mrow> <mrow> <mo> &#8970; </mo> <mrow> <mo> - </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> a </mi> <mn> 0 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mo> &#8971; </mo> </mrow> <mo> + </mo> <msub> <mi> a </mi> <mn> 0 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, RowBox[List[TagBox[&quot;s&quot;, Zeta, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[RowBox[List[RowBox[List[&quot;\[LeftFloor]&quot;, RowBox[List[&quot;-&quot;, RowBox[List[&quot;Re&quot;, &quot;(&quot;, SubscriptBox[&quot;a&quot;, &quot;0&quot;], &quot;)&quot;]]]], &quot;\[RightFloor]&quot;]], &quot;+&quot;, SubscriptBox[&quot;a&quot;, &quot;0&quot;], &quot;+&quot;, &quot;1&quot;]], Zeta, Rule[Editable, True], Rule[Selectable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[List[ZetaDump`e1$, ZetaDump`e2$], Zeta[ZetaDump`e1$, ZetaDump`e2$]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mo> + </mo> <semantics> <mrow> <mi> &#950; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Zeta", "[", RowBox[List["s_", ",", "a_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Zeta", "[", RowBox[List["s", ",", SubscriptBox["aa", "0"]]], "]"]], "-", RowBox[List["Zeta", "[", RowBox[List["s", ",", RowBox[List["1", "+", RowBox[List["Floor", "[", RowBox[List["-", RowBox[List["Re", "[", SubscriptBox["aa", "0"], "]"]]]], "]"]], "+", SubscriptBox["aa", "0"]]]]], "]"]], "+", RowBox[List["Zeta", "[", RowBox[List["s", ",", RowBox[List[RowBox[List["Max", "[", RowBox[List["0", ",", RowBox[List["1", "+", RowBox[List["Floor", "[", RowBox[List["-", RowBox[List["Re", "[", SubscriptBox["aa", "0"], "]"]]]], "]"]]]]]], "]"]], "+", SubscriptBox["aa", "0"]]]]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["a", "-", SubscriptBox["aa", "0"]]], "]"]]]], ")"]]]]]]]]










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





2007-05-02





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