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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 n > Involving power function





http://functions.wolfram.com/04.06.21.0006.01









  


  








Input Form





Integrate[(1/n) Mod[m, n], n] == m (Log[n] - 1) + Mod[m, n]








Standard Form





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








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> <mfrac> <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> <mi> n </mi> </mfrac> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> n </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> m </mi> </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> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> n </ci> </bvar> <apply> <times /> <apply> <rem /> <ci> $CellContext`m </ci> <ci> $CellContext`n </ci> </apply> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <ln /> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> <ci> m </ci> </apply> <apply> <rem /> <ci> $CellContext`m </ci> <ci> $CellContext`n </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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


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





2001-10-29