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http://functions.wolfram.com/03.02.09.0001.01
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BesselI[\[Nu], z] == Limit[\[Lambda]^\[Nu] LegendreP[\[Lambda], -\[Nu], 3,
Cosh[z/\[Lambda]]], \[Lambda] -> Infinity]
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Cell[BoxData[RowBox[List[RowBox[List["BesselI", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List["Limit", "[", RowBox[List[RowBox[List[SuperscriptBox["\[Lambda]", "\[Nu]"], " ", RowBox[List["LegendreP", "[", RowBox[List["\[Lambda]", ",", RowBox[List["-", "\[Nu]"]], ",", "3", ",", RowBox[List["Cosh", "[", FractionBox["z", "\[Lambda]"], "]"]]]], "]"]]]], ",", RowBox[List["\[Lambda]", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]]
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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> <msub> <mi> I </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <munder> <mi> lim </mi> <mrow> <mi> λ </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <mrow> <msup> <mi> λ </mi> <mi> ν </mi> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mstyle scriptlevel='0'> <msubsup> <mi> 𝔓 </mi> <mi> λ </mi> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> </msubsup> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mi> λ </mi> </mfrac> <mo> ) </mo> </mrow> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[StyleBox[SubsuperscriptBox[TagBox["\[GothicCapitalP]", LegendreQ], "\[Lambda]", RowBox[List["-", "\[Nu]"]]], Rule[ScriptLevel, 0]], "(", StyleBox[RowBox[List["cosh", "(", FractionBox["z", "\[Lambda]"], ")"]], Rule[ScriptLevel, 0]], StyleBox[")", Rule[ScriptLevel, 0]]]], LegendreP] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <msub> <mi> I </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <munder> <mi> lim </mi> <mrow> <mi> λ </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <mrow> <msup> <mi> λ </mi> <mi> ν </mi> </msup> <mo> ⁢ </mo> <semantics> <mrow> <mstyle scriptlevel='0'> <msubsup> <mi> 𝔓 </mi> <mi> λ </mi> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> </msubsup> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mi> λ </mi> </mfrac> <mo> ) </mo> </mrow> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[StyleBox[SubsuperscriptBox[TagBox["\[GothicCapitalP]", LegendreQ], "\[Lambda]", RowBox[List["-", "\[Nu]"]]], Rule[ScriptLevel, 0]], "(", StyleBox[RowBox[List["cosh", "(", FractionBox["z", "\[Lambda]"], ")"]], Rule[ScriptLevel, 0]], StyleBox[")", Rule[ScriptLevel, 0]]]], LegendreP] </annotation> </semantics> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BesselI", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Limit", "[", RowBox[List[RowBox[List[SuperscriptBox["\[Lambda]", "\[Nu]"], " ", RowBox[List["LegendreP", "[", RowBox[List["\[Lambda]", ",", RowBox[List["-", "\[Nu]"]], ",", "3", ",", RowBox[List["Cosh", "[", FractionBox["z", "\[Lambda]"], "]"]]]], "]"]]]], ",", RowBox[List["\[Lambda]", "\[Rule]", "\[Infinity]"]]]], "]"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
