DLMF:14.12.E13 (Q4834)

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DLMF:14.12.E13
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    Statements

    Defining formula
    𝑸 n ⁡ ( x ) = 1 2 ⁢ ( n ! ) ⁢ ∫ - 1 1 P n ⁡ ( t ) x - t ⁢ d t . shorthand-associated-Legendre-black-Q 𝑛 𝑥 1 2 𝑛 superscript subscript 1 1 Legendre-spherical-polynomial 𝑛 𝑡 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle\boldsymbol{Q}_{n}\left(x\right)=\frac{1}{2(n!)}% \int_{-1}^{1}\frac{P_{n}\left(t\right)}{x-t}\mathrm{d}t.}}
    0 references
    DLMF id
    DLMF:14.12.E13
    0 references
    Symbols used
    Q10920
    Defining formula
    P n ⁡ ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r10.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5addec
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