DLMF:14.12.E7 (Q4828)

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DLMF:14.12.E7
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    Statements

    test
    P ν m ⁡ ( x ) = ( ν + 1 ) m π ⁢ ∫ 0 π ( x + ( x 2 - 1 ) 1 / 2 ⁢ cos ⁡ ϕ ) ν ⁢ cos ⁡ ( m ⁢ ϕ ) ⁢ d ϕ , Legendre-P-first-kind 𝑚 𝜈 𝑥 Pochhammer 𝜈 1 𝑚 𝜋 superscript subscript 0 𝜋 superscript 𝑥 superscript superscript 𝑥 2 1 1 2 italic-ϕ 𝜈 𝑚 italic-ϕ italic-ϕ {\displaystyle{\displaystyle P^{m}_{\nu}\left(x\right)=\frac{{\left(\nu+1% \right)_{m}}}{\pi}\*\int_{0}^{\pi}\left(x+\left(x^{2}-1\right)^{1/2}\cos\phi% \right)^{\nu}\cos\left(m\phi\right)\mathrm{d}\phi,}}
    0 references
    DLMF id
    DLMF:14.12.E7
    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.m1abdec
    0 references
     
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