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Prime




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/13.03.17.0001.01









  


  








Input Form





Sin[Pi Prime[n]]^2 + Sin[(Pi (1 + Gamma[Prime[n]]))/Prime[n]]^2 == 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", RowBox[List["Prime", "[", "n", "]"]]]], "]"]], "2"], "+", SuperscriptBox[RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["Gamma", "[", RowBox[List["Prime", "[", "n", "]"]], "]"]]]], ")"]]]], RowBox[List["Prime", "[", "n", "]"]]], "]"]], "2"]]], "\[Equal]", "0"]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> prime </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> prime </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mi> prime </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <power /> <apply> <sin /> <apply> <times /> <pi /> <apply> <plus /> <apply> <ci> Gamma </ci> <apply> <ci> prime </ci> <ci> n </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> prime </ci> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <sin /> <apply> <times /> <pi /> <apply> <ci> prime </ci> <ci> n </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", RowBox[List["Prime", "[", "n_", "]"]]]], "]"]], "2"], "+", SuperscriptBox[RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["Gamma", "[", RowBox[List["Prime", "[", "n_", "]"]], "]"]]]], ")"]]]], RowBox[List["Prime", "[", "n_", "]"]]], "]"]], "2"]]], "]"]], "\[RuleDelayed]", "0"]]]]


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





2001-10-29