DLMF:10.14.E5 (Q3142): Difference between revisions

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Property / constraint
 

ν 0 , 0 < x 1 formulae-sequence 𝜈 0 0 𝑥 1 {\displaystyle{\displaystyle\nu\geq 0,0<x\leq 1}}

\nu\geq 0,0<x\leq 1
Property / constraint: ν 0 , 0 < x 1 formulae-sequence 𝜈 0 0 𝑥 1 {\displaystyle{\displaystyle\nu\geq 0,0<x\leq 1}} / rank
 
Normal rank

Revision as of 17:17, 30 December 2019

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DLMF:10.14.E5
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    | J ν ( ν x ) | x ν exp ( ν ( 1 - x 2 ) 1 2 ) ( 1 + ( 1 - x 2 ) 1 2 ) ν , Bessel-J 𝜈 𝜈 𝑥 superscript 𝑥 𝜈 𝜈 superscript 1 superscript 𝑥 2 1 2 superscript 1 superscript 1 superscript 𝑥 2 1 2 𝜈 {\displaystyle{\displaystyle|J_{\nu}\left(\nu x\right)|\leq\frac{x^{\nu}\exp% \left(\nu(1-x^{2})^{\frac{1}{2}}\right)}{\left(1+(1-x^{2})^{\frac{1}{2}}\right% )^{\nu}},}}
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    ν 0 , 0 < x 1 formulae-sequence 𝜈 0 0 𝑥 1 {\displaystyle{\displaystyle\nu\geq 0,0<x\leq 1}}
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