DLMF:14.12.E12 (Q4833)

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DLMF:14.12.E12
No description defined

    Statements

    test
    𝑸 n m ⁡ ( x ) = 1 ( n - m ) ! ⁢ P n m ⁡ ( x ) ⁢ ∫ x ∞ d t ( t 2 - 1 ) ⁢ ( P n m ⁡ ( t ) ) 2 , associated-Legendre-black-Q 𝑚 𝑛 𝑥 1 𝑛 𝑚 Legendre-P-first-kind 𝑚 𝑛 𝑥 superscript subscript 𝑥 𝑡 superscript 𝑡 2 1 superscript Legendre-P-first-kind 𝑚 𝑛 𝑡 2 {\displaystyle{\displaystyle\boldsymbol{Q}^{m}_{n}\left(x\right)=\frac{1}{(n-m% )!}P^{m}_{n}\left(x\right)\int_{x}^{\infty}\frac{\mathrm{d}t}{\left(t^{2}-1% \right)\left(\displaystyle P^{m}_{n}\left(t\right)\right)^{2}},}}
    0 references
    DLMF id
    DLMF:14.12.E12
    0 references
    constraint
    n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    0 references
    Symbols used
    Q11481
    test
    P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m1addec
    0 references
    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.m3acdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ajdec
    0 references
    Q11589
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1idec
    0 references
    Q11593
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S1.XMD5.m1ddec
    0 references
    Q11602
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1cdec
    0 references
     
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