InverseGammaRegularized[a, Infinity, z] == InverseGammaRegularized[a, -z]

Cell[BoxData[RowBox[List[RowBox[List["InverseGammaRegularized", "[", RowBox[List["a", ",", "\[Infinity]", ",", "z"]], "]"]], "\[Equal]", RowBox[List["InverseGammaRegularized", "[", RowBox[List["a", ",", RowBox[List["-", "z"]]]], "]"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <semantics> <mi> Q </mi> <annotation-xml encoding='MathML-Content'> <ci> GammaRegularized </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> &#8734; </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msup> <semantics> <mi> Q </mi> <annotation-xml encoding='MathML-Content'> <ci> GammaRegularized </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> InverseGammaRegularized </ci> <ci> a </ci> <infinity /> <ci> z </ci> </apply> <apply> <ci> InverseGammaRegularized </ci> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseGammaRegularized", "[", RowBox[List["a_", ",", "\[Infinity]", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["InverseGammaRegularized", "[", RowBox[List["a", ",", RowBox[List["-", "z"]]]], "]"]]]]]]

2001-10-29