DLMF:14.12.E14 (Q4835)

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DLMF:14.12.E14
No description defined

    Statements

    Defining formula
    𝑸 n ⁡ ( x ) = 1 n ! ⁢ ∫ 0 ∞ d t ( x + ( x 2 - 1 ) 1 / 2 ⁢ cosh ⁡ t ) n + 1 . shorthand-associated-Legendre-black-Q 𝑛 𝑥 1 𝑛 superscript subscript 0 𝑡 superscript 𝑥 superscript superscript 𝑥 2 1 1 2 𝑡 𝑛 1 {\displaystyle{\displaystyle\boldsymbol{Q}_{n}\left(x\right)=\frac{1}{n!}\int_% {0}^{\infty}\frac{\mathrm{d}t}{\left(x+(x^{2}-1)^{1/2}\cosh t\right)^{n+1}}.}}
    0 references
    DLMF id
    DLMF:14.12.E14
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aedec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2addec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aldec
    0 references
    Q11597
    Defining formula
    𝑸 ν ⁡ ( z ) = 𝑸 ν 0 ⁡ ( z ) shorthand-associated-Legendre-black-Q 𝜈 𝑧 associated-Legendre-black-Q 0 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}_{\NVar{\nu}}\left(\NVar{z}\right)=% \boldsymbol{Q}^{0}_{\nu}\left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m6aadec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1kdec
    0 references
    Q11602
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1edec
    0 references
     
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