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Cosh




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.20.26.0002.01









  


  








Input Form





Cosh[z]^2 == 1/2 + (1/2) Hypergeometric0F1[1/2, z^2]








Standard Form





Cell[BoxData[RowBox[List[SuperscriptBox[RowBox[List["Cosh", "[", "z", "]"]], "2"], "\[Equal]", RowBox[List[FractionBox["1", "2"], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Hypergeometric0F1", "[", RowBox[List[FractionBox["1", "2"], ",", SuperscriptBox["z", "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> <msup> <mi> cosh </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <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> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </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;1&quot;, &quot;2&quot;], Hypergeometric0F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False]], &quot;;&quot;, TagBox[SuperscriptBox[&quot;z&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> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <apply> <cosh /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <ci> Hypergeometric0F1 </ci> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["Cosh", "[", "z_", "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Hypergeometric0F1", "[", RowBox[List[FractionBox["1", "2"], ",", SuperscriptBox["z", "2"]]], "]"]]]]]]]]]]


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





2001-10-29