DLMF:10.23.E19 (Q3473): Difference between revisions

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‎Changed an Item: Add constraint
‎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.m2amdec

Revision as of 13:32, 2 January 2020

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DLMF:10.23.E19
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    Statements

    Defining formula
    a m = 2 ( J ν + 1 ⁡ ( j ν , m ) ) 2 ⁢ ∫ 0 1 t ⁢ f ⁢ ( t ) ⁢ J ν ⁡ ( j ν , m ⁢ t ) ⁢ d t , subscript 𝑎 𝑚 2 superscript Bessel-J 𝜈 1 zero-Bessel-J 𝜈 𝑚 2 superscript subscript 0 1 𝑡 𝑓 𝑡 Bessel-J 𝜈 subscript 𝑗 𝜈 𝑚 𝑡 𝑡 {\displaystyle{\displaystyle a_{m}=\frac{2}{(J_{\nu+1}\left(j_{\nu,m}\right))^% {2}}\int_{0}^{1}tf(t)J_{\nu}\left(j_{\nu,m}t\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:10.23.E19
    0 references
    constraint
    ν ≥ - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\nu\geq-\tfrac{1}{2}}}
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2amdec
    0 references
     
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