SphericalHankelH1[\[Nu], z] == Sqrt[Pi/2] (1/Sqrt[z]) HankelH1[\[Nu] + 1/2, z]

Cell[BoxData[RowBox[List[RowBox[List["SphericalHankelH1", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SqrtBox[FractionBox["\[Pi]", "2"]], FractionBox["1", SqrtBox["z"]], RowBox[List["HankelH1", "[", RowBox[List[RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ",", "z"]], "]"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msubsup> <semantics> <mi> h </mi> <annotation encoding='Mathematica'> TagBox[&quot;h&quot;, SphericalHankelH1] </annotation> </semantics> <mi> &#957; </mi> <mrow> <mo> ( </mo> <mn> 1 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <msqrt> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> </msqrt> <mo> &#8290; </mo> <mfrac> <mrow> <mn> 1 </mn> <mtext> </mtext> </mrow> <msqrt> <mi> z </mi> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <msubsup> <semantics> <mi> H </mi> <annotation encoding='Mathematica'> TagBox[&quot;H&quot;, HankelH1] </annotation> </semantics> <mrow> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mrow> <mo> ( </mo> <mn> 1 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> SphericalHankelH1 </ci> <ci> &#957; </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HankelH1 </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SphericalHankelH1", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["HankelH1", "[", RowBox[List[RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ",", "z"]], "]"]]]], SqrtBox["z"]]]]]]

2007-05-02