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Pi




Mathematica Notation

Traditional Notation









Constants > Pi > Representations through more general functions > Through other functions





http://functions.wolfram.com/02.03.26.0003.01









  


  








Input Form





Pi == 4 (ArcTan[(q - p)/(p + q)] + ArcTan[p/q]) /; Element[p, Integers] && p > 0 && Element[q, Integers] && q > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Pi]", "\[Equal]", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["ArcTan", "[", FractionBox[RowBox[List["q", "-", "p"]], RowBox[List["p", "+", "q"]]], "]"]], "+", RowBox[List["ArcTan", "[", FractionBox["p", "q"], "]"]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["p", "\[Element]", "Integers"]], "\[And]", RowBox[List["p", ">", "0"]], "\[And]", RowBox[List["q", "\[Element]", "Integers"]], "\[And]", RowBox[List["q", ">", "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> <mi> &#960; </mi> <mo> &#10869; </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mi> p </mi> <mi> q </mi> </mfrac> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> q </mi> <mo> - </mo> <mi> p </mi> </mrow> <mrow> <mi> p </mi> <mo> + </mo> <mi> q </mi> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> p </mi> <mo> &#8712; </mo> <msup> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> <mo> + </mo> </msup> </mrow> <mo> &#8743; </mo> <mrow> <mi> q </mi> <mo> &#8712; </mo> <msup> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> <mo> + </mo> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <pi /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <arctan /> <apply> <times /> <ci> p </ci> <apply> <power /> <ci> q </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <arctan /> <apply> <times /> <apply> <plus /> <ci> q </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> p </ci> <ci> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> p </ci> <apply> <ci> SuperPlus </ci> <integers /> </apply> </apply> <apply> <in /> <ci> q </ci> <apply> <ci> SuperPlus </ci> <integers /> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "\[Pi]", "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["ArcTan", "[", FractionBox[RowBox[List["q", "-", "p"]], RowBox[List["p", "+", "q"]]], "]"]], "+", RowBox[List["ArcTan", "[", FractionBox["p", "q"], "]"]]]], ")"]]]], "/;", RowBox[List[RowBox[List["p", "\[Element]", "Integers"]], "&&", RowBox[List["p", ">", "0"]], "&&", RowBox[List["q", "\[Element]", "Integers"]], "&&", RowBox[List["q", ">", "0"]]]]]]]]]]


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





2001-10-29