DLMF:14.6.E7 (Q4749)

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DLMF:14.6.E7
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    Statements

    Defining formula
    P ν - m ⁡ ( x ) = ( x 2 - 1 ) - m / 2 ⁢ ∫ 1 x … ⁢ ∫ 1 x P ν ⁡ ( x ) ⁢ ( d x ) m , Legendre-P-first-kind 𝑚 𝜈 𝑥 superscript superscript 𝑥 2 1 𝑚 2 superscript subscript 1 𝑥 … superscript subscript 1 𝑥 shorthand-Legendre-P-first-kind 𝜈 𝑥 superscript 𝑥 𝑚 {\displaystyle{\displaystyle P^{-m}_{\nu}\left(x\right)=\left(x^{2}-1\right)^{% -m/2}\int_{1}^{x}\!\dots\!\int_{1}^{x}P_{\nu}\left(x\right)\left(\!\mathrm{d}x% \right)^{m},}}
    0 references
    DLMF id
    DLMF:14.6.E7
    0 references
    Symbols used
    Q11481
    Defining formula
    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.m1aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
     
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