DLMF:14.7.E15 (Q4767)

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DLMF:14.7.E15
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    Statements

    Defining formula
    P m m ⁡ ( x ) = ( 2 ⁢ m ) ! 2 m ⁢ m ! ⁢ ( x 2 - 1 ) m / 2 . Legendre-P-first-kind 𝑚 𝑚 𝑥 2 𝑚 superscript 2 𝑚 𝑚 superscript superscript 𝑥 2 1 𝑚 2 {\displaystyle{\displaystyle P^{m}_{m}\left(x\right)=\frac{(2m)!}{2^{m}m!}% \left(x^{2}-1\right)^{m/2}.}}
    0 references
    DLMF id
    DLMF:14.7.E15
    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.m1acdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aedec
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    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1ndec
    0 references
    Q11593
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S1.XMD5.m1fdec
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