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http://functions.wolfram.com/03.21.03.0042.01
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SphericalBesselJ[\[Nu], DirectedInfinity[E^(I \[Lambda])]] ==
Piecewise[{{0, \[Lambda] == 0 || \[Lambda] == Pi}}, ComplexInfinity] /;
Im[\[Lambda]] == 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]", ",", RowBox[List["DirectedInfinity", "[", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Lambda]"]]], "]"]]]], "]"]], "\[Equal]", RowBox[List["Piecewise", "[", RowBox[List[RowBox[List["{", RowBox[List["{", RowBox[List["0", ",", RowBox[List[RowBox[List["\[Lambda]", "\[Equal]", "0"]], "||", RowBox[List["\[Lambda]", "\[Equal]", "\[Pi]"]]]]]], "}"]], "}"]], ",", " ", "ComplexInfinity"]], "]"]]]], "/;", RowBox[List[RowBox[List["Im", "[", "\[Lambda]", "]"]], "\[Equal]", "0"]]]]]]
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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> <mrow> <msub> <mi> j </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> λ </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> ∞ </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mo>  </mo> <mtable> <mtr> <mtd> <mn> 0 </mn> </mtd> <mtd> <mrow> <mrow> <mi> λ </mi> <mo>  </mo> <mn> 0 </mn> </mrow> <mo> ∨ </mo> <mrow> <mi> λ </mi> <mo>  </mo> <mi> π </mi> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mo> ~ </mo> </mtd> <mtd> <semantics> <mi> True </mi> <annotation encoding='Mathematica'> TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]] </annotation> </semantics> </mtd> </mtr> </mtable> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> λ </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <msub> <mi> j </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> λ </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> ∞ </mi> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mo>  </mo> <mtable> <mtr> <mtd> <mn> 0 </mn> </mtd> <mtd> <mrow> <mrow> <mi> λ </mi> <mo>  </mo> <mn> 0 </mn> </mrow> <mo> ∨ </mo> <mrow> <mi> λ </mi> <mo>  </mo> <mi> π </mi> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mo> ~ </mo> </mtd> <mtd> <semantics> <mi> True </mi> <annotation encoding='Mathematica'> TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]] </annotation> </semantics> </mtd> </mtr> </mtable> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> λ </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mn> 0 </mn> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]_", ",", RowBox[List["DirectedInfinity", "[", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Lambda]_"]]], "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Piecewise]", GridBox[List[List["0", RowBox[List[RowBox[List["\[Lambda]", "\[Equal]", "0"]], "||", RowBox[List["\[Lambda]", "\[Equal]", "\[Pi]"]]]]], List["ComplexInfinity", TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]]]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 1.2`], Rule[ColumnWidths, Automatic]]]], "/;", RowBox[List[RowBox[List["Im", "[", "\[Lambda]", "]"]], "\[Equal]", "0"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
