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http://functions.wolfram.com/06.08.20.0011.01
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D[GammaRegularized[a, z], a] == MeijerG[{{}, {1, 1}}, {{0, 0, a}, {}}, z]/
Gamma[a] + GammaRegularized[a, z] (Log[z] - PolyGamma[a])
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Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "a"], RowBox[List["GammaRegularized", "[", RowBox[List["a", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", "1"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "0", ",", "a"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z"]], "]"]], RowBox[List["Gamma", "[", "a", "]"]]], "+", RowBox[List[RowBox[List["GammaRegularized", "[", RowBox[List["a", ",", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List["PolyGamma", "[", "a", "]"]]]], ")"]]]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <mo> ∂ </mo> <mrow> <semantics> <mi> Q </mi> <annotation-xml encoding='MathML-Content'> <ci> GammaRegularized </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <mi> a </mi> </mrow> </mfrac> <mo>  </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mfrac> <mo> ⁢ </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mi> a </mi> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "3"]], RowBox[List["3", ",", "0"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox["1", MeijerG, Rule[Editable, True]], ",", TagBox["1", MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox["a", MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </mrow> <mo> + </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> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> a </ci> </bvar> <apply> <ci> GammaRegularized </ci> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <ci> Gamma </ci> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> MeijerG </ci> <list> <list /> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 1 </cn> </list> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> <ci> a </ci> </list> <list /> </list> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <ci> GammaRegularized </ci> <ci> a </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <ln /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> PolyGamma </ci> <ci> a </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["a_"]]], RowBox[List["GammaRegularized", "[", RowBox[List["a_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", "1"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "0", ",", "a"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z"]], "]"]], RowBox[List["Gamma", "[", "a", "]"]]], "+", RowBox[List[RowBox[List["GammaRegularized", "[", RowBox[List["a", ",", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List["PolyGamma", "[", "a", "]"]]]], ")"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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