DLMF:14.8.E15 (Q4789)

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DLMF:14.8.E15
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    Statements

    Defining formula
    𝑸 ν μ ⁡ ( x ) ∼ π 1 / 2 Γ ⁡ ( ν + 3 2 ) ⁢ ( 2 ⁢ x ) ν + 1 , asymptotically-equals associated-Legendre-black-Q 𝜇 𝜈 𝑥 superscript 𝜋 1 2 Euler-Gamma 𝜈 3 2 superscript 2 𝑥 𝜈 1 {\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu}\left(x\right)\sim\frac{% \pi^{1/2}}{\Gamma\left(\nu+\frac{3}{2}\right)(2x)^{\nu+1}},}}
    0 references
    DLMF id
    DLMF:14.8.E15
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    constraint
    ν ≠ - 3 2 , - 5 2 , - 7 2 , … 𝜈 3 2 5 2 7 2 … {\displaystyle{\displaystyle\nu\neq-\tfrac{3}{2},-\tfrac{5}{2},-\tfrac{7}{2},% \dots}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2akdec
    0 references
    Q11592
    Defining formula
    𝑸 ν μ ⁡ ( z ) associated-Legendre-black-Q 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m3aadec
    0 references
     
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