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variants of this functions
InverseGammaRegularized




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > InverseGammaRegularized[a,z1,z2] > Integration > Indefinite integration > Involving one direct function with respect to z2





http://functions.wolfram.com/06.13.21.0001.01









  


  








Input Form





Integrate[InverseGammaRegularized[a, Subscript[z, 1], Subscript[z, 2]], Subscript[z, 2]] == (-a) GammaRegularized[a + 1, InverseGammaRegularized[a, Subscript[z, 1], Subscript[z, 2]]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["InverseGammaRegularized", "[", RowBox[List["a", ",", SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]], RowBox[List["\[DifferentialD]", SubscriptBox["z", "2"]]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", "a"]], " ", RowBox[List["GammaRegularized", "[", RowBox[List[RowBox[List["a", "+", "1"]], ",", RowBox[List["InverseGammaRegularized", "[", RowBox[List["a", ",", SubscriptBox["z", "1"], ",", 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> <mo> &#8747; </mo> <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> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> &#8290; </mo> <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> <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> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </bvar> <apply> <ci> InverseGammaRegularized </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> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <ci> GammaRegularized </ci> <apply> <plus /> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> InverseGammaRegularized </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> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["InverseGammaRegularized", "[", RowBox[List["a_", ",", SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "]"]], RowBox[List["\[DifferentialD]", SubscriptBox["z_", "2"]]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "a"]], " ", RowBox[List["GammaRegularized", "[", RowBox[List[RowBox[List["a", "+", "1"]], ",", RowBox[List["InverseGammaRegularized", "[", RowBox[List["a", ",", SubscriptBox["zz", "1"], ",", SubscriptBox["zz", "2"]]], "]"]]]], "]"]]]]]]]]


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





2001-10-29