DLMF:10.22.E35 (Q3409): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aahdec

Revision as of 13:18, 2 January 2020

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DLMF:10.22.E35
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    Statements

    Defining formula
    ∫ 0 x J μ ⁡ ( t ) ⁢ J ν ⁡ ( x - t ) ⁢ d t t ⁢ ( x - t ) = ( μ + ν ) ⁢ J μ + ν ⁡ ( x ) μ ⁢ ν ⁢ x , superscript subscript 0 𝑥 Bessel-J 𝜇 𝑡 Bessel-J 𝜈 𝑥 𝑡 𝑡 𝑡 𝑥 𝑡 𝜇 𝜈 Bessel-J 𝜇 𝜈 𝑥 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\int_{0}^{x}\frac{J_{\mu}\left(t\right)J_{\nu}% \left(x-t\right)\mathrm{d}t}{t(x-t)}=\frac{(\mu+\nu)J_{\mu+\nu}\left(x\right)}% {\mu\nu x},}}
    0 references
    DLMF id
    DLMF:10.22.E35
    0 references
    constraint
    ℜ ⁡ μ > 0 , ℜ ⁡ ν > 0 formulae-sequence 𝜇 0 𝜈 0 {\displaystyle{\displaystyle\Re\mu>0,\Re\nu>0}}
    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.m2aaadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aahdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aahdec
    0 references
     
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