DLMF:10.21.E38 (Q3338): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: Bessel function of the first kind / qualifier
 
Defining formula:

J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

\BesselJ{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Bessel function of the first kind / qualifier
 
xml-id: C10.S2.E2.m2addec

Revision as of 15:45, 2 January 2020

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DLMF:10.21.E38
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    Statements

    J ν ( j ν , m ) ( - 1 ) m - 1 ( 2 / ν ) 1 3 π N ( a m ) k = 0 β k ν 2 k / 3 , asymptotic-expansion Bessel-J 𝜈 diffop zero-Bessel-J 𝜈 𝑚 1 superscript 1 𝑚 1 superscript 2 𝜈 1 3 𝜋 modulus-Airy-N zero-derivative-Airy-Ai 𝑚 superscript subscript 𝑘 0 subscript superscript 𝛽 𝑘 superscript 𝜈 2 𝑘 3 {\displaystyle{\displaystyle J_{\nu}\left(j_{\nu,m}'\right)\sim(-1)^{m-1}\frac% {(2/\nu)^{\frac{1}{3}}}{\pi N\left(a^{\prime}_{m}\right)}\sum_{k=0}^{\infty}% \frac{\beta^{\prime}_{k}}{\nu^{2k/3}},}}
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    DLMF:10.21.E38
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    J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E2.m2addec
    0 references