Degree: Representations through more general functions (formula 02.04.26.0010)

Degree

$Mathematica Notation$

Constants

Degree

Representations through more general functions

Through other functions

http://functions.wolfram.com/02.04.26.0010.01

Input Form

Degree == (1/45) (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["Degree", "\[Equal]", RowBox[List[FractionBox["1", "45"], " ", 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> <mo> ° </mo> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 45 </mn> </mfrac> <mo> ⁢ </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> ∈ </mo> <msup> <semantics> <mi> ℕ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalN]", Function[Integers]] </annotation> </semantics> <mo> + </mo> </msup> </mrow> <mo> ∧ </mo> <mrow> <mi> q </mi> <mo> ∈ </mo> <msup> <semantics> <mi> ℕ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalN]", Function[Integers]] </annotation> </semantics> <mo> + </mo> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <ci> Degree </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 45 </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", "[", "\[Degree]", "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "45"], " ", 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)

2007-05-02