BesselI[\[Nu], DirectedInfinity[E^(I \[Lambda])]] == Piecewise[{{0, Abs[\[Lambda]] == Pi/2}}, ComplexInfinity] /; Im[\[Lambda]] == 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> I </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <semantics> <mrow> <mtext> </mtext> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> </msup> <mo> &#8290; </mo> <mi> &#8734; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> DirectedInfinity </ci> <cn type='complex-cartesian'> 1 <sep /> 1 </cn> </apply> </annotation-xml> </semantics> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mo> &#62305; </mo> <mtable> <mtr> <mtd> <mn> 0 </mn> </mtd> <mtd> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> &#955; </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &#63449; </mo> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> </mtd> <mtd> <semantics> <mi> True </mi> <annotation encoding='Mathematica'> TagBox[&quot;True&quot;, &quot;PiecewiseDefault&quot;, Rule[AutoDelete, False], Rule[DeletionWarning, True]] </annotation> </semantics> </mtd> </mtr> </mtable> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#955; </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> BesselI </ci> <ci> &#957; </ci> <apply> <ci> DirectedInfinity </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> </apply> </apply> <piecewise> <piece> <cn type='integer'> 0 </cn> <apply> <eq /> <apply> <abs /> <ci> &#955; </ci> </apply> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </piece> <otherwise> <apply> <ci> OverTilde </ci> <infinity /> </apply> </otherwise> </piecewise> </apply> <apply> <eq /> <apply> <imaginary /> <ci> &#955; </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

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2007-05-02