DLMF:10.9.E19 (Q3088): Difference between revisions

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imported>Admin
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
 
test:

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.m2aidec

Revision as of 14:15, 2 January 2020

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DLMF:10.9.E19
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    Statements

    J ν ( z ) = ( 1 2 z ) ν 2 π i - ( 0 + ) exp ( t - z 2 4 t ) d t t ν + 1 , Bessel-J 𝜈 𝑧 superscript 1 2 𝑧 𝜈 2 𝜋 𝑖 superscript subscript limit-from 0 𝑡 superscript 𝑧 2 4 𝑡 𝑡 superscript 𝑡 𝜈 1 {\displaystyle{\displaystyle J_{\nu}\left(z\right)=\frac{(\tfrac{1}{2}z)^{\nu}% }{2\pi i}\int_{-\infty}^{(0+)}\exp\left(t-\frac{z^{2}}{4t}\right)\frac{\mathrm% {d}t}{t^{\nu+1}},}}
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    J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E2.m2aidec
    0 references