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variants of this functions
Zeta




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > Zeta[s,a] > General characteristics > Domain and analyticity > Domain and analyticity > For zeta(s,a)





http://functions.wolfram.com/10.02.04.0001.01









  


  








Input Form





DomainAndRange[Function[{(Editable -> True)[s], (Editable -> True)[a]}, Zeta[(Editable -> True)[s], (Editable -> True)[a]]]] == ProductSet[Complexes, Complexes] \[LongRightArrow] Complexes








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List[TagBox["s", Rule[Editable, True]], ",", TagBox["a", Rule[Editable, True]]]], "}"]], ",", RowBox[List["Zeta", "[", RowBox[List[TagBox["s", Rule[Editable, True]], ",", TagBox["a", Rule[Editable, True]]]], "]"]]]], "]"]], "]"]], " ", "\[Equal]", "\[IndentingNewLine]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["Complexes", ",", "Complexes"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]








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> <mo> ( </mo> <mrow> <mi> s </mi> <mo> &#8902; </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <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> </mrow> <mo> &#8759; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#8450; </mi> <mo> &#8855; </mo> <mi> &#8450; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <mi> &#8450; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportion </ci> <apply> <ci> LongRightArrow </ci> <apply> <ci> Star </ci> <ci> s </ci> <ci> a </ci> </apply> <apply> <ci> Zeta </ci> <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> <apply> <ci> LongRightArrow </ci> <apply> <ci> CircleTimes </ci> <ci> &#8450; </ci> <ci> &#8450; </ci> </apply> <ci> &#8450; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["Editable", "\[Rule]", "True"]], ")"]], "[", "s_", "]"]], ",", RowBox[List[RowBox[List["(", RowBox[List["Editable", "\[Rule]", "True"]], ")"]], "[", "a_", "]"]]]], "}"]], ",", RowBox[List["Zeta", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["Editable", "\[Rule]", "True"]], ")"]], "[", "s_", "]"]], ",", RowBox[List[RowBox[List["(", RowBox[List["Editable", "\[Rule]", "True"]], ")"]], "[", "a_", "]"]]]], "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["Complexes", ",", "Complexes"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]


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





2001-10-29