DLMF:11.11.E15 (Q4081): Difference between revisions

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Property / constraint
 

0 < λ < 1 0 𝜆 1 {\displaystyle{\displaystyle 0<\lambda<1}}

0<\lambda<1
Property / constraint: 0 < λ < 1 0 𝜆 1 {\displaystyle{\displaystyle 0<\lambda<1}} / rank
 
Normal rank

Revision as of 16:43, 30 December 2019

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DLMF:11.11.E15
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    Statements

    𝐀 - ν ( λ ν ) ( 2 π ν ) 1 / 2 ( 1 + 1 - λ 2 λ ) ν e - ν 1 - λ 2 ( 1 - λ 2 ) 1 / 4 , asymptotically-equals associated-Anger-Weber-A 𝜈 𝜆 𝜈 superscript 2 𝜋 𝜈 1 2 superscript 1 1 superscript 𝜆 2 𝜆 𝜈 superscript 𝑒 𝜈 1 superscript 𝜆 2 superscript 1 superscript 𝜆 2 1 4 {\displaystyle{\displaystyle\mathbf{A}_{-\nu}\left(\lambda\nu\right)\sim\left(% \frac{2}{\pi\nu}\right)^{1/2}\left(\frac{1+\sqrt{1-\lambda^{2}}}{\lambda}% \right)^{\nu}\frac{e^{-\nu\sqrt{1-\lambda^{2}}}}{(1-\lambda^{2})^{1/4}},}}
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    0 < λ < 1 0 𝜆 1 {\displaystyle{\displaystyle 0<\lambda<1}}
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