DLMF:14.17.E6 (Q4887)

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DLMF:14.17.E6
No description defined

    Statements

    Defining formula
    ∫ - 1 1 𝖯 l m ⁡ ( x ) ⁢ 𝖯 n m ⁡ ( x ) ⁢ d x = ( n + m ) ! ( n - m ) ! ⁢ ( n + 1 2 ) ⁢ δ l , n , superscript subscript 1 1 Ferrers-Legendre-P-first-kind 𝑚 𝑙 𝑥 Ferrers-Legendre-P-first-kind 𝑚 𝑛 𝑥 𝑥 𝑛 𝑚 𝑛 𝑚 𝑛 1 2 Kronecker 𝑙 𝑛 {\displaystyle{\displaystyle\int_{-1}^{1}\mathsf{P}^{m}_{l}\left(x\right)% \mathsf{P}^{m}_{n}\left(x\right)\mathrm{d}x=\frac{(n+m)!}{(n-m)!\left(n+\frac{% 1}{2}\right)}\delta_{l,n},}}
    0 references
    DLMF id
    DLMF:14.17.E6
    0 references
    Symbols used
    Ferrers function of the first kind
    Defining formula
    𝖯 ν μ ⁡ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E1.m2aedec
    0 references
    Q10768
    Defining formula
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aedec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1edec
    0 references
    Q11593
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S1.XMD5.m1dec
    0 references
    Q11602
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1dec
    0 references
    Q11622
    Defining formula
    l 𝑙 {\displaystyle{\displaystyle l}}
    xml-id
    C14.S17.XMD1.m1dec
    0 references
     
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