DLMF:10.23.E20 (Q3474)

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DLMF:10.23.E20
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    Statements

    Defining formula
    1 2 ⁢ f ⁢ ( x - ) + 1 2 ⁢ f ⁢ ( x + ) = ∑ m = 1 ∞ a m ⁢ J ν ⁡ ( j ν , m ⁢ x ) , 1 2 𝑓 limit-from 𝑥 1 2 𝑓 limit-from 𝑥 superscript subscript 𝑚 1 subscript 𝑎 𝑚 Bessel-J 𝜈 subscript 𝑗 𝜈 𝑚 𝑥 {\displaystyle{\displaystyle\tfrac{1}{2}f(x-)+\tfrac{1}{2}f(x+)=\sum_{m=1}^{% \infty}a_{m}J_{\nu}\left(j_{\nu,m}x\right),}}
    0 references
    DLMF id
    DLMF:10.23.E20
    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.m2andec
    0 references
    Q11438
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C10.S1.XMD1.m1adec
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    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1adec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1hdec
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    DLMF:10.23.E11
    Defining formula
    a k subscript 𝑎 𝑘 {\displaystyle{\displaystyle a_{k}}}
    xml-id
    C10.S23.XMD2.m1ddec
    0 references
    Q11476
    Defining formula
    f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}
    xml-id
    C10.S23.XMD3.m1edec
    0 references
     
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