|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/04.06.20.0007.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
D[Mod[m, n], {n, \[Alpha]}] == Mod[m, n]/(n^\[Alpha] Gamma[2 - \[Alpha]]) -
(m \[Alpha])/(n^\[Alpha] Gamma[2 - \[Alpha]])
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["n", ",", "\[Alpha]"]], "}"]]], RowBox[List["Mod", "[", RowBox[List["m", ",", "n"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["n", RowBox[List["-", "\[Alpha]"]]], " ", RowBox[List["Mod", "[", RowBox[List["m", ",", "n"]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List["2", "-", "\[Alpha]"]], "]"]]], "-", FractionBox[RowBox[List["m", " ", "\[Alpha]", " ", SuperscriptBox["n", RowBox[List["-", "\[Alpha]"]]]]], RowBox[List["Gamma", "[", RowBox[List["2", "-", "\[Alpha]"]], "]"]]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <msup> <mo> ∂ </mo> <mi> α </mi> </msup> <mrow> <mo> ( </mo> <semantics> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mi> n </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <ci> FE`Conversion`Private`n </ci> </apply> </annotation-xml> </semantics> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <msup> <mi> n </mi> <mi> α </mi> </msup> </mrow> </mfrac> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <msup> <mi> n </mi> <mrow> <mo> - </mo> <mi> α </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <semantics> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mi> n </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <ci> FE`Conversion`Private`n </ci> </apply> </annotation-xml> </semantics> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> α </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mi> α </mi> <mo> ⁢ </mo> <msup> <mi> n </mi> <mrow> <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> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> n </ci> <degree> <ci> α </ci> </degree> </bvar> <apply> <rem /> <ci> $CellContext`m </ci> <ci> FE`Conversion`Private`n </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> α </ci> </apply> </apply> <apply> <rem /> <ci> $CellContext`m </ci> <ci> FE`Conversion`Private`n </ci> </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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> m </ci> <ci> α </ci> <apply> <power /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> α </ci> </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> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["n_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["Mod", "[", RowBox[List["m_", ",", "n_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["n", RowBox[List["-", "\[Alpha]"]]], " ", RowBox[List["Mod", "[", RowBox[List["m", ",", "n"]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List["2", "-", "\[Alpha]"]], "]"]]], "-", FractionBox[RowBox[List["m", " ", "\[Alpha]", " ", SuperscriptBox["n", RowBox[List["-", "\[Alpha]"]]]]], RowBox[List["Gamma", "[", RowBox[List["2", "-", "\[Alpha]"]], "]"]]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|