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Mod




Mathematica Notation

Traditional Notation









Integer Functions > Mod[m,n] > Integration > Indefinite integration > Involving one direct function and elementary functions with respect to m > Involving power function





http://functions.wolfram.com/04.06.21.0002.01









  


  








Input Form





Integrate[m^(\[Alpha] - 1) Mod[m, n], m] == (m^\[Alpha] ((\[Alpha] + 1) Mod[m, n] - m))/(\[Alpha] (\[Alpha] + 1))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["m", RowBox[List["\[Alpha]", "-", "1"]]], RowBox[List["Mod", "[", RowBox[List["m", ",", "n"]], "]"]], RowBox[List["\[DifferentialD]", "m"]]]]]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox["m", "\[Alpha]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["\[Alpha]", "+", "1"]], ")"]], " ", RowBox[List["Mod", "[", RowBox[List["m", ",", "n"]], "]"]]]], "-", "m"]], ")"]]]], RowBox[List["\[Alpha]", " ", RowBox[List["(", RowBox[List["\[Alpha]", "+", "1"]], ")"]]]]]]]]]








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> <mi> m </mi> <mrow> <mi> &#945; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <semantics> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <ci> $CellContext`n </ci> </apply> </annotation-xml> </semantics> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> m </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mrow> <msup> <mi> m </mi> <mi> &#945; </mi> </msup> <mtext> </mtext> </mrow> <mrow> <mi> &#945; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#945; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#945; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <semantics> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <ci> $CellContext`n </ci> </apply> </annotation-xml> </semantics> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> m </ci> </bvar> <apply> <times /> <apply> <power /> <ci> m </ci> <apply> <plus /> <ci> &#945; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <rem /> <ci> $CellContext`m </ci> <ci> $CellContext`n </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <ci> m </ci> <ci> &#945; </ci> </apply> <apply> <power /> <apply> <times /> <ci> &#945; </ci> <apply> <plus /> <ci> &#945; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> &#945; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <rem /> <ci> $CellContext`m </ci> <ci> $CellContext`n </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["m_", RowBox[List["\[Alpha]_", "-", "1"]]], " ", RowBox[List["Mod", "[", RowBox[List["m_", ",", "n_"]], "]"]]]], RowBox[List["\[DifferentialD]", "m_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["m", "\[Alpha]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["\[Alpha]", "+", "1"]], ")"]], " ", RowBox[List["Mod", "[", RowBox[List["m", ",", "n"]], "]"]]]], "-", "m"]], ")"]]]], RowBox[List["\[Alpha]", " ", RowBox[List["(", RowBox[List["\[Alpha]", "+", "1"]], ")"]]]]]]]]]


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





2001-10-29