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HypergeometricU




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricU[a,b,z] > General characteristics > Symmetries and periodicities > Mirror symmetry





http://functions.wolfram.com/07.33.04.0002.01









  


  








Input Form





HypergeometricU[Conjugate[a], Conjugate[b], Conjugate[z]] == Conjugate[HypergeometricU[a, b, z]] /; !IntervalMemberQ[Interval[{-Infinity, 0}], z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List[RowBox[List["Conjugate", "[", "a", "]"]], ",", RowBox[List["Conjugate", "[", "b", "]"]], ",", RowBox[List["Conjugate", "[", "z", "]"]]]], "]"]], "\[Equal]", RowBox[List["Conjugate", "[", RowBox[List["HypergeometricU", "[", RowBox[List["a", ",", "b", ",", "z"]], "]"]], "]"]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]], "]"]]]]]]








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> <semantics> <mi> U </mi> <annotation encoding='Mathematica'> TagBox[&quot;U&quot;, HypergeometricU] </annotation> </semantics> <mo> ( </mo> <mrow> <mover> <mi> a </mi> <mo> _ </mo> </mover> <mo> , </mo> <mover> <mi> b </mi> <mo> _ </mo> </mover> <mo> , </mo> <mover> <mi> z </mi> <mo> _ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mover> <semantics> <mrow> <mi> U </mi> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[TagBox[&quot;U&quot;, HypergeometricU], &quot;(&quot;, RowBox[List[&quot;a&quot;, &quot;,&quot;, &quot;b&quot;, &quot;,&quot;, &quot;z&quot;]], &quot;)&quot;]], BernoulliB] </annotation> </semantics> <mo> _ </mo> </mover> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <semantics> <mi> U </mi> <annotation encoding='Mathematica'> TagBox[&quot;U&quot;, HypergeometricU] </annotation> </semantics> <mo> ( </mo> <mrow> <mover> <mi> a </mi> <mo> _ </mo> </mover> <mo> , </mo> <mover> <mi> b </mi> <mo> _ </mo> </mover> <mo> , </mo> <mover> <mi> z </mi> <mo> _ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mover> <semantics> <mrow> <mi> U </mi> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[TagBox[&quot;U&quot;, HypergeometricU], &quot;(&quot;, RowBox[List[&quot;a&quot;, &quot;,&quot;, &quot;b&quot;, &quot;,&quot;, &quot;z&quot;]], &quot;)&quot;]], BernoulliB] </annotation> </semantics> <mo> _ </mo> </mover> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricU", "[", RowBox[List[RowBox[List["Conjugate", "[", "a_", "]"]], ",", RowBox[List["Conjugate", "[", "b_", "]"]], ",", RowBox[List["Conjugate", "[", "z_", "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Conjugate", "[", RowBox[List["HypergeometricU", "[", RowBox[List["a", ",", "b", ",", "z"]], "]"]], "]"]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]


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





2001-10-29