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http://functions.wolfram.com/11.10.25.0001.01
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Limit[SpheroidalS1[\[Nu], \[Mu], \[Gamma], z/\[Gamma]]/
SphericalBesselJ[\[Nu], z], z -> Infinity] == 1
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Cell[BoxData[RowBox[List[RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List["SpheroidalS1", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "\[Gamma]", ",", FractionBox["z", "\[Gamma]"]]], "]"]], RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]], ",", RowBox[List["z", "\[Rule]", "\[Infinity]"]]]], "]"]], "\[Equal]", "1"]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <munder> <mi> lim </mi> <mrow> <mi> z </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <mfrac> <semantics> <mrow> <msubsup> <mi> S </mi> <mrow> <mi> ν </mi> <mo> , </mo> <mi> μ </mi> </mrow> <mrow> <mo> ( </mo> <mn> 1 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mrow> <mi> γ </mi> <mo> , </mo> <mfrac> <mi> z </mi> <mi> γ </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox["S", RowBox[List[TagBox["\[Nu]", SpheroidalS1, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["\[Mu]", SpheroidalS1, Rule[Editable, True], Rule[Selectable, True]]]], RowBox[List["(", "1", ")"]]], "(", RowBox[List[TagBox["\[Gamma]", SpheroidalS1, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["z", "\[Gamma]"], SpheroidalS1, Rule[Editable, True], Rule[Selectable, True]]]], ")"]], InterpretTemplate[Function[SpheroidalS1[SlotSequence[1]]]], Rule[Editable, False], Rule[Selectable, False]] </annotation> </semantics> <mrow> <msub> <mi> j </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo>  </mo> <mn> 1 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <limit /> <bvar> <ci> z </ci> </bvar> <condition> <apply> <tendsto /> <ci> z </ci> <infinity /> </apply> </condition> <apply> <times /> <apply> <ci> SpheroidalS1 </ci> <ci> ν </ci> <ci> μ </ci> <ci> γ </ci> <apply> <times /> <ci> z </ci> <apply> <power /> <ci> γ </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> SphericalBesselJ </ci> <ci> ν </ci> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[FractionBox[RowBox[List["SpheroidalS1", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "\[Gamma]_", ",", FractionBox["z_", "\[Gamma]_"]]], "]"]], RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]]], ",", RowBox[List["z_", "\[Rule]", "\[Infinity]"]]]], "]"]], "]"]], "\[RuleDelayed]", "1"]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
