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http://functions.wolfram.com/10.02.20.0054.01
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Derivative[0, 2][Zeta][s, a] == s (s + 1) Zeta[2 + s, a] /;
!(Element[-a, Integers] && -a >= 0)
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["Zeta", TagBox[RowBox[List["(", RowBox[List["0", ",", "2"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["s", ",", "a"]], "]"]], "\[Equal]", RowBox[List["s", RowBox[List["(", RowBox[List["s", "+", "1"]], ")"]], RowBox[List["Zeta", "[", RowBox[List[RowBox[List["2", "+", "s"]], ",", "a"]], "]"]]]]]], "/;", RowBox[List["Not", "[", RowBox[List[RowBox[List["Element", "[", RowBox[List[RowBox[List["-", "a"]], ",", "Integers"]], "]"]], "\[And]", RowBox[List[RowBox[List["-", "a"]], "\[GreaterEqual]", "0"]]]], "]"]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msup> <mi> ζ </mi> <semantics> <mrow> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", RowBox[List["0", ",", "2"]], ")"]], Derivative] </annotation> </semantics> </msup> <mo> ( </mo> <mrow> <mi> s </mi> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mi> s </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> s </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> s </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", RowBox[List[TagBox[RowBox[List["s", "+", "2"]], Zeta, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["a", Zeta, Rule[Editable, True], Rule[Selectable, True]]]], ")"]], InterpretTemplate[Function[List[ZetaDump`e1$, ZetaDump`e2$], Zeta[ZetaDump`e1$, ZetaDump`e2$]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> ∉ </mo> <mi> ℕ </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 2 </cn> </list> <ci> Zeta </ci> </apply> <ci> s </ci> <ci> a </ci> </apply> <apply> <times /> <ci> s </ci> <apply> <plus /> <ci> s </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Zeta </ci> <apply> <plus /> <ci> s </ci> <cn type='integer'> 2 </cn> </apply> <ci> a </ci> </apply> </apply> </apply> <apply> <notin /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <ci> ℕ </ci> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox["Zeta", TagBox[RowBox[List["(", RowBox[List["0", ",", "2"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["s_", ",", "a_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["s", " ", RowBox[List["(", RowBox[List["s", "+", "1"]], ")"]], " ", RowBox[List["Zeta", "[", RowBox[List[RowBox[List["2", "+", "s"]], ",", "a"]], "]"]]]], "/;", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "a"]], "\[GreaterEqual]", "0"]]]], ")"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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