DLMF:14.8.E2 (Q4776)

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DLMF:14.8.E2
No description defined

    Statements

    Defining formula
    𝖯 ν m ⁡ ( x ) ∼ ( - 1 ) m ⁢ ( ν - m + 1 ) 2 ⁢ m m ! ⁢ ( 1 - x 2 ) m / 2 , asymptotically-equals Ferrers-Legendre-P-first-kind 𝑚 𝜈 𝑥 superscript 1 𝑚 Pochhammer 𝜈 𝑚 1 2 𝑚 𝑚 superscript 1 𝑥 2 𝑚 2 {\displaystyle{\displaystyle\mathsf{P}^{m}_{\nu}\left(x\right)\sim(-1)^{m}% \frac{{\left(\nu-m+1\right)_{2m}}}{m!}\left(\frac{1-x}{2}\right)^{m/2},}}
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    DLMF id
    DLMF:14.8.E2
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    constraint
    ν ≠ m - 1 , m - 2 , … , - m 𝜈 𝑚 1 𝑚 2 … 𝑚 {\displaystyle{\displaystyle\nu\neq m-1,m-2,\dots,-m}}
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    Symbols used
    Ferrers function of the first kind
    Defining formula
    𝖯 ν μ ⁡ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E1.m2aadec
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    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
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    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2aadec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1adec
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    Q11593
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S1.XMD5.m1dec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1adec
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