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variants of this functions
GammaRegularized




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > GammaRegularized[a,z1,z2] > General characteristics > Symmetries and periodicities > Mirror symmetry





http://functions.wolfram.com/06.09.04.0002.01









  


  








Input Form





GammaRegularized[Conjugate[a], Conjugate[Subscript[z, 1]], Conjugate[Subscript[z, 2]]] == Conjugate[GammaRegularized[a, Subscript[z, 1], Subscript[z, 2]]] /; !IntervalMemberQ[Interval[{-Infinity, 0}], Subscript[z, 1]] && !IntervalMemberQ[Interval[{-Infinity, 0}], Subscript[z, 2]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["GammaRegularized", "[", RowBox[List[RowBox[List["Conjugate", "[", "a", "]"]], ",", RowBox[List["Conjugate", "[", SubscriptBox["z", "1"], "]"]], ",", RowBox[List["Conjugate", "[", SubscriptBox["z", "2"], "]"]]]], "]"]], "\[Equal]", RowBox[List["Conjugate", "[", RowBox[List["GammaRegularized", "[", RowBox[List["a", ",", SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]], "]"]]]], "/;", RowBox[List[RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", " ", SubscriptBox["z", "1"]]], "]"]], "]"]], "\[And]", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", " ", SubscriptBox["z", "2"]]], "]"]], "]"]]]]]]]]








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> <semantics> <mi> Q </mi> <annotation-xml encoding='MathML-Content'> <ci> GammaRegularized </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mover> <mi> a </mi> <mo> _ </mo> </mover> <mo> , </mo> <mover> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> _ </mo> </mover> <mo> , </mo> <mover> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> _ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mover> <mrow> <semantics> <mi> Q </mi> <annotation-xml encoding='MathML-Content'> <ci> GammaRegularized </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> _ </mo> </mover> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <semantics> <mi> Q </mi> <annotation-xml encoding='MathML-Content'> <ci> GammaRegularized </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mover> <mi> a </mi> <mo> _ </mo> </mover> <mo> , </mo> <mover> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> _ </mo> </mover> <mo> , </mo> <mover> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> _ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mover> <mrow> <semantics> <mi> Q </mi> <annotation-xml encoding='MathML-Content'> <ci> GammaRegularized </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> _ </mo> </mover> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["GammaRegularized", "[", RowBox[List[RowBox[List["Conjugate", "[", "a_", "]"]], ",", RowBox[List["Conjugate", "[", SubscriptBox["z_", "1"], "]"]], ",", RowBox[List["Conjugate", "[", SubscriptBox["z_", "2"], "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Conjugate", "[", RowBox[List["GammaRegularized", "[", RowBox[List["a", ",", SubscriptBox["zz", "1"], ",", SubscriptBox["zz", "2"]]], "]"]], "]"]], "/;", RowBox[List[RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", SubscriptBox["zz", "1"]]], "]"]]]], "&&", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", SubscriptBox["zz", "2"]]], "]"]]]]]]]]]]]]


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





2001-10-29