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Floor




Mathematica Notation

Traditional Notation









Integer Functions > Floor[z] > Differentiation > Fractional integro-differentiation





http://functions.wolfram.com/04.01.20.0003.01









  


  








Input Form





D[Floor[z], {z, \[Alpha]}] == Floor[z]/(z^\[Alpha] Gamma[1 - \[Alpha]])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "\[Alpha]"]], "}"]]], RowBox[List["Floor", "[", "z", "]"]]]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["Floor", "[", "z", "]"]], SuperscriptBox["z", RowBox[List["-", "\[Alpha]"]]]]], RowBox[List[" ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Alpha]"]], "]"]]]]]]]]]








MathML Form







<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> &#8706; </mo> <mi> &#945; </mi> </msup> <mrow> <mo> &#8970; </mo> <mi> z </mi> <mo> &#8971; </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> z </mi> <mi> &#945; </mi> </msup> </mrow> </mfrac> <mo> &#10869; </mo> <mfrac> <mrow> <mrow> <mo> &#8970; </mo> <mi> z </mi> <mo> &#8971; </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mi> &#945; </mi> </mrow> </msup> </mrow> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#945; </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <ci> &#945; </ci> </degree> </bvar> <apply> <floor /> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <floor /> <ci> z </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </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["z_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["Floor", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Floor", "[", "z", "]"]], " ", SuperscriptBox["z", RowBox[List["-", "\[Alpha]"]]]]], RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Alpha]"]], "]"]]]]]]]


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





2001-10-29