Real part: Differentiation (formula 12.03.20.0002)

$Mathematica Notation$

Complex Components

Re[z]

Differentiation

Fractional integro-differentiation

http://functions.wolfram.com/12.03.20.0002.01

Input Form

D[Re[x], {x, \[Alpha]}] == x^(1 - \[Alpha])/Gamma[2 - \[Alpha]] /; Element[x, Reals]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["x", ",", "\[Alpha]"]], "}"]]], RowBox[List["Re", "[", "x", "]"]]]], "\[Equal]", FractionBox[SuperscriptBox["x", RowBox[List["1", "-", "\[Alpha]"]]], RowBox[List["Gamma", "[", RowBox[List["2", "-", "\[Alpha]"]], "]"]]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mfrac> <mrow> <msup> <mo> ∂ </mo> <mi> α </mi> </msup> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <msup> <mi> x </mi> <mi> α </mi> </msup> </mrow> </mfrac> <mo> ⩵ </mo> <mfrac> <mrow> <mtext> </mtext> <msup> <mi> x </mi> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> α </mi> </mrow> </msup> </mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> α </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[Reals]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> x </ci> <degree> <ci> α </ci> </degree> </bvar> <apply> <real /> <ci> x </ci> </apply> </apply> <apply> <times /> <apply> <power /> <ci> x </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> α </ci> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> α </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <in /> <ci> x </ci> <reals /> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["x_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["Re", "[", "x_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox["x", RowBox[List["1", "-", "\[Alpha]"]]], RowBox[List["Gamma", "[", RowBox[List["2", "-", "\[Alpha]"]], "]"]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]]]

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

2001-10-29