DLMF:10.14.E6 (Q3143): Difference between revisions

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

\nu>0,0<x\leq 1
Property / constraint: ν > 0 , 0 < x 1 formulae-sequence 𝜈 0 0 𝑥 1 {\displaystyle{\displaystyle\nu>0,0<x\leq 1}} / rank
 
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Revision as of 17:17, 30 December 2019

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DLMF:10.14.E6
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    | J ν ( ν x ) | ( 1 + x 2 ) 1 4 x ( 2 π ν ) 1 2 x ν exp ( ν ( 1 - x 2 ) 1 2 ) ( 1 + ( 1 - x 2 ) 1 2 ) ν , diffop Bessel-J 𝜈 1 𝜈 𝑥 superscript 1 superscript 𝑥 2 1 4 𝑥 superscript 2 𝜋 𝜈 1 2 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{(1+x^{2})^{% \frac{1}{4}}}{x(2\pi\nu)^{\frac{1}{2}}}\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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    DLMF:10.14.E6
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    ν > 0 , 0 < x 1 formulae-sequence 𝜈 0 0 𝑥 1 {\displaystyle{\displaystyle\nu>0,0<x\leq 1}}
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