DLMF:14.12.E11 (Q4832)

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DLMF:14.12.E11
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    Statements

    test
    𝑸 n m ⁡ ( x ) = ( x 2 - 1 ) m / 2 2 n + 1 ⁢ n ! ⁢ ∫ - 1 1 ( 1 - t 2 ) n ( x - t ) n + m + 1 ⁢ d t , associated-Legendre-black-Q 𝑚 𝑛 𝑥 superscript superscript 𝑥 2 1 𝑚 2 superscript 2 𝑛 1 𝑛 superscript subscript 1 1 superscript 1 superscript 𝑡 2 𝑛 superscript 𝑥 𝑡 𝑛 𝑚 1 𝑡 {\displaystyle{\displaystyle\boldsymbol{Q}^{m}_{n}\left(x\right)=\frac{\left(x% ^{2}-1\right)^{m/2}}{2^{n+1}n!}\int_{-1}^{1}\frac{\left(1-t^{2}\right)^{n}}{(x% -t)^{n+m+1}}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:14.12.E11
    0 references
    Symbols used
    Q11592
    test
    𝑸 ν μ ⁡ ( z ) associated-Legendre-black-Q 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m3abdec
    0 references
     
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