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variants of this functions
Gamma




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Gamma[z] > Transformations > Products, sums, and powers of the direct function > Products of the direct function





http://functions.wolfram.com/06.05.16.0016.01









  


  








Input Form





Gamma[z]/Gamma[w] == (z - w)! Binomial[z - 1, z - w]








Standard Form





Cell[BoxData[RowBox[List[FractionBox[RowBox[List["Gamma", "[", "z", "]"]], RowBox[List["Gamma", "[", "w", "]"]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["z", "-", "w"]], ")"]], "!"]], RowBox[List["Binomial", "[", RowBox[List[RowBox[List["z", "-", "1"]], ",", RowBox[List["z", "-", "w"]]]], "]"]]]]]]]]








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> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> w </mi> <mo> ) </mo> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi> z </mi> <mo> - </mo> <mi> w </mi> </mrow> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[RowBox[List[&quot;z&quot;, &quot;-&quot;, &quot;1&quot;]], Identity, Rule[Editable, True]]], List[TagBox[RowBox[List[&quot;z&quot;, &quot;-&quot;, &quot;w&quot;]], Identity, Rule[Editable, True]]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <ci> Gamma </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <ci> w </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <factorial /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[RowBox[List["Gamma", "[", "z_", "]"]], RowBox[List["Gamma", "[", "w_", "]"]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["z", "-", "w"]], ")"]], "!"]], " ", RowBox[List["Binomial", "[", RowBox[List[RowBox[List["z", "-", "1"]], ",", RowBox[List["z", "-", "w"]]]], "]"]]]]]]]]


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





2001-10-29