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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Representations through more general functions > Through hypergeometric functions > Involving 0F1





http://functions.wolfram.com/01.07.26.0003.01









  


  










Input Form





Cos[z] == (-(z - Pi/2)) Hypergeometric0F1[3/2, (-(1/4)) (z - Pi/2)^2]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Cos", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["z", "-", FractionBox["\[Pi]", "2"]]], ")"]]]], " ", RowBox[List["Hypergeometric0F1", "[", RowBox[List[FractionBox["3", "2"], ",", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", FractionBox["\[Pi]", "2"]]], ")"]], "2"]]]]], "]"]]]]]]]]










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> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 0 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mo> &#8202; </mo> <mo> ; </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;0&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;1&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[&quot;\[Null]&quot;, InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[TagBox[FractionBox[&quot;3&quot;, &quot;2&quot;], Hypergeometric0F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False]], &quot;;&quot;, TagBox[RowBox[List[RowBox[List[&quot;-&quot;, FractionBox[&quot;1&quot;, &quot;4&quot;]]], &quot; &quot;, SuperscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;z&quot;, &quot;-&quot;, FractionBox[&quot;\[Pi]&quot;, &quot;2&quot;]]], &quot;)&quot;]], &quot;2&quot;]]], Hypergeometric0F1, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric0F1] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <cos /> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Hypergeometric0F1 </ci> <cn type='rational'> 3 <sep /> 2 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cos", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["z", "-", FractionBox["\[Pi]", "2"]]], ")"]]]], " ", RowBox[List["Hypergeometric0F1", "[", RowBox[List[FractionBox["3", "2"], ",", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", FractionBox["\[Pi]", "2"]]], ")"]], "2"]]]]], "]"]]]]]]]]










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





2001-10-29