|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/01.02.21.0004.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Integrate[a^(\[Alpha] - 1) z^a, a] ==
((-a^\[Alpha]) Gamma[\[Alpha], (-a) Log[z]])/((-a) Log[z])^\[Alpha]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["a", RowBox[List["\[Alpha]", "-", "1"]]], SuperscriptBox["z", "a"], RowBox[List["\[DifferentialD]", "a"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", SuperscriptBox["a", "\[Alpha]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], " ", RowBox[List["Log", "[", "z", "]"]]]], ")"]], RowBox[List["-", "\[Alpha]"]]], " ", RowBox[List["Gamma", "[", RowBox[List["\[Alpha]", ",", RowBox[List[RowBox[List["-", "a"]], " ", RowBox[List["Log", "[", "z", "]"]]]]]], "]"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> ∫ </mo> <mrow> <mrow> <msup> <mi> a </mi> <mrow> <mi> α </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> a </mi> </msup> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> a </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <msup> <mi> a </mi> <mi> α </mi> </msup> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> α </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> α </mi> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> a </ci> </bvar> <apply> <times /> <apply> <power /> <ci> a </ci> <apply> <plus /> <ci> α </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> a </ci> <ci> α </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <ln /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> α </ci> </apply> </apply> <apply> <ci> Gamma </ci> <ci> α </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["a_", RowBox[List["\[Alpha]_", "-", "1"]]], " ", SuperscriptBox["z_", "a_"]]], RowBox[List["\[DifferentialD]", "a_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", SuperscriptBox["a", "\[Alpha]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], " ", RowBox[List["Log", "[", "z", "]"]]]], ")"]], RowBox[List["-", "\[Alpha]"]]], " ", RowBox[List["Gamma", "[", RowBox[List["\[Alpha]", ",", RowBox[List[RowBox[List["-", "a"]], " ", RowBox[List["Log", "[", "z", "]"]]]]]], "]"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
){kind=small}
