DLMF:18.17.E2 (Q5743)

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DLMF:18.17.E2
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    Statements

    Defining formula
    ∫ 0 x L m ⁡ ( y ) ⁢ L n ⁡ ( x - y ) ⁢ d y = ∫ 0 x L m + n ⁡ ( y ) ⁢ d y = L m + n ⁡ ( x ) - L m + n + 1 ⁡ ( x ) . superscript subscript 0 𝑥 shorthand-Laguerre-polynomial-L 𝑚 𝑦 shorthand-Laguerre-polynomial-L 𝑛 𝑥 𝑦 𝑦 superscript subscript 0 𝑥 shorthand-Laguerre-polynomial-L 𝑚 𝑛 𝑦 𝑦 shorthand-Laguerre-polynomial-L 𝑚 𝑛 𝑥 shorthand-Laguerre-polynomial-L 𝑚 𝑛 1 𝑥 {\displaystyle{\displaystyle\int_{0}^{x}L_{m}\left(y\right)L_{n}\left(x-y% \right)\mathrm{d}y=\int_{0}^{x}L_{m+n}\left(y\right)\mathrm{d}y=L_{m+n}\left(x% \right)-L_{m+n+1}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.17.E2
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q10921
    Defining formula
    L n ⁡ ( x ) = L n ( 0 ) ⁡ ( x ) shorthand-Laguerre-polynomial-L 𝑛 𝑥 Laguerre-polynomial-L 0 𝑛 𝑥 {\displaystyle{\displaystyle L_{\NVar{n}}\left(\NVar{x}\right)=L^{(0)}_{n}% \left(x\right)}}
    xml-id
    C18.S1.I1.ix7.p1.m3adec
    0 references
     
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