DLMF:10.23.E19 (Q3473)

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DLMF:10.23.E19
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    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,}}
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    DLMF:10.23.E19
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    ν - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\nu\geq-\tfrac{1}{2}}}
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    J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E2.m2amdec
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1abdec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3abdec
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