DLMF:10.22.E11 (Q3385): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1ajdec

Revision as of 15:49, 2 January 2020

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DLMF:10.22.E11
No description defined

    Statements

    test
    ∫ 0 x 1 - J 0 ⁡ ( t ) t ⁢ d t = 1 2 ⁢ ∑ k = 1 ∞ ψ ⁡ ( k + 1 ) - ψ ⁡ ( 1 ) k ! ⁢ ( 1 2 ⁢ x ) k ⁢ J k ⁡ ( x ) , superscript subscript 0 𝑥 1 Bessel-J 0 𝑡 𝑡 𝑡 1 2 superscript subscript 𝑘 1 digamma 𝑘 1 digamma 1 𝑘 superscript 1 2 𝑥 𝑘 Bessel-J 𝑘 𝑥 {\displaystyle{\displaystyle\int_{0}^{x}\frac{1-J_{0}\left(t\right)}{t}\mathrm% {d}t=\frac{1}{2}\sum_{k=1}^{\infty}\frac{\psi\left(k+1\right)-\psi\left(1% \right)}{k!}(\tfrac{1}{2}x)^{k}J_{k}\left(x\right),}}
    0 references
    DLMF id
    DLMF:10.22.E11
    0 references
    Symbols used
    Bessel function of the first kind
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2acdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
    0 references
     
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