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Prime




Mathematica Notation

Traditional Notation









Number Theory Functions > Prime[n] > Identities > Functional identities





http://functions.wolfram.com/13.03.17.0002.01









  


  








Input Form





(E^((2 Pi I Gamma[p])/p) - 1)/(E^(-((2 Pi I)/p)) - 1) == 1 /; Element[p, Primes]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]", " ", RowBox[List["Gamma", "[", "p", "]"]]]], "p"]], "-", "1"]], RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "p"]]]], "-", "1"]]], "\[Equal]", "1"]], "/;", " ", RowBox[List["p", "\[Element]", "Primes"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mfrac> <mrow> <msup> <mi> &#8519; </mi> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> p </mi> <mo> ) </mo> </mrow> </mrow> <mi> p </mi> </mfrac> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> <mi> p </mi> </mfrac> </mrow> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#10869; </mo> <mn> 1 </mn> </mrow> <mo> /; </mo> <mrow> <mi> p </mi> <mo> &#8712; </mo> <semantics> <mi> &#8473; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalP]&quot;, Function[Primes]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <apply> <plus /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> <imaginaryi /> <apply> <ci> Gamma </ci> <ci> p </ci> </apply> <apply> <power /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> <imaginaryi /> <apply> <power /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <in /> <ci> p </ci> <primes /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]", " ", RowBox[List["Gamma", "[", "p_", "]"]]]], "p_"]], "-", "1"]], RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "p_"]]]], "-", "1"]]], "]"]], "\[RuleDelayed]", RowBox[List["1", "/;", RowBox[List["p", "\[Element]", "Primes"]]]]]]]]


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





2001-10-29