GammaRegularized[a + 1, Subscript[z, 1], Subscript[z, 2]] == GammaRegularized[a, Subscript[z, 1], Subscript[z, 2]] - (1/Gamma[a + 1]) (Subscript[z, 2]^a/E^Subscript[z, 2] - Subscript[z, 1]^a/E^Subscript[z, 1])

Cell[BoxData[RowBox[List[RowBox[List["GammaRegularized", "[", RowBox[List[RowBox[List["a", "+", "1"]], ",", SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["GammaRegularized", "[", RowBox[List["a", ",", SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]], "-", RowBox[List[FractionBox["1", RowBox[List["Gamma", "[", RowBox[List["a", "+", "1"]], "]"]]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", SubscriptBox["z", "2"]]]], " ", SubsuperscriptBox["z", "2", "a"]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", SubscriptBox["z", "1"]]]], " ", SubsuperscriptBox["z", "1", "a"]]]]], ")"]]]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mi> Q </mi> <annotation-xml encoding='MathML-Content'> <ci> GammaRegularized </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <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> &#10869; </mo> <mrow> <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> <mfrac> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> </msup> <mo> &#8290; </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mi> a </mi> </msubsup> </mrow> <mo> - </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> </msup> <mo> &#8290; </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mi> a </mi> </msubsup> </mrow> </mrow> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> GammaRegularized </ci> <apply> <plus /> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <ci> GammaRegularized </ci> <ci> a </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["GammaRegularized", "[", RowBox[List[RowBox[List["a_", "+", "1"]], ",", SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["GammaRegularized", "[", RowBox[List["a", ",", SubscriptBox["zz", "1"], ",", SubscriptBox["zz", "2"]]], "]"]], "-", FractionBox[RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", SubscriptBox["zz", "2"]]]], " ", SubsuperscriptBox["zz", "2", "a"]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", SubscriptBox["zz", "1"]]]], " ", SubsuperscriptBox["zz", "1", "a"]]]]], RowBox[List["Gamma", "[", RowBox[List["a", "+", "1"]], "]"]]]]]]]]]

2001-10-29