DLMF:10.22.E33 (Q3407): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1udec

Latest revision as of 13:18, 2 January 2020

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DLMF:10.22.E33
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    Statements

    Defining formula
    ∫ 0 x J ν ⁡ ( t ) ⁢ J - ν ⁡ ( x - t ) ⁢ d t = sin ⁡ x , superscript subscript 0 𝑥 Bessel-J 𝜈 𝑡 Bessel-J 𝜈 𝑥 𝑡 𝑡 𝑥 {\displaystyle{\displaystyle\int_{0}^{x}J_{\nu}\left(t\right)J_{-\nu}\left(x-t% \right)\mathrm{d}t=\sin x,}}
    0 references
    DLMF id
    DLMF:10.22.E33
    0 references
    constraint
    | ℜ ⁡ ν | < 1 𝜈 1 {\displaystyle{\displaystyle|\Re\nu|<1}}
    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.m2aydec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aafdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aafdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1ardec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aldec
    0 references
    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1kdec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1udec
    0 references
     
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