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Round




Mathematica Notation

Traditional Notation









Integer Functions > Round[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving power function





http://functions.wolfram.com/04.03.21.0002.01









  


  








Input Form





Integrate[z^(\[Alpha] - 1) Round[z], z] == (z^\[Alpha]/\[Alpha]) Round[z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", RowBox[List["\[Alpha]", "-", "1"]]], " ", RowBox[List["Round", "[", "z", "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox["z", "\[Alpha]"], "\[Alpha]"], RowBox[List["Round", "[", "z", "]"]]]]]]]]








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> <msup> <mi> z </mi> <mrow> <mi> &#945; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <mtext> </mtext> <mrow> <mo> &#8970; </mo> <mi> z </mi> <mo> &#8969; </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <msup> <mi> z </mi> <mi> &#945; </mi> </msup> <mo> &#8290; </mo> <mtext> </mtext> <mrow> <mo> &#8970; </mo> <mi> z </mi> <mo> &#8969; </mo> </mrow> </mrow> <mi> &#945; </mi> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> &#8747; </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> ErrorBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> SuperscriptBox </ci> <ms> z </ms> <apply> <ci> RowBox </ci> <list> <ms> &#945; </ms> <ms> - </ms> <ms> 1 </ms> </list> </apply> </apply> <ms> &#8970;z&#8969; </ms> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> &#8518; </ms> <ms> z </ms> </list> </apply> </list> </apply> </list> </apply> <ms> &#10869; </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> SuperscriptBox </ci> <ms> z </ms> <ms> &#945; </ms> </apply> <ms> &#8970;z&#8969; </ms> </list> </apply> <ms> &#945; </ms> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", RowBox[List["\[Alpha]_", "-", "1"]]], " ", RowBox[List["Round", "[", "z_", "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["z", "\[Alpha]"], " ", RowBox[List["Round", "[", "z", "]"]]]], "\[Alpha]"]]]]]


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





2001-10-29