DLMF:14.20.E7 (Q4928)

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DLMF:14.20.E7
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    Statements

    Defining formula
    𝖰 ^ - 1 2 + i ⁢ τ μ ⁡ ( x ) ∼ 1 2 ⁢ Γ ⁡ ( μ ) ⁢ ( 2 1 - x ) μ / 2 , asymptotically-equals Ferrers-conical-legendre-Q-hat 𝜇 1 2 𝑖 𝜏 𝑥 1 2 Euler-Gamma 𝜇 superscript 2 1 𝑥 𝜇 2 {\displaystyle{\displaystyle\widehat{\mathsf{Q}}^{\mu}_{-\frac{1}{2}+i\tau}% \left(x\right)\sim\tfrac{1}{2}\Gamma\left(\mu\right)\left(\frac{2}{1-x}\right)% ^{\mu/2},}}
    0 references
    DLMF id
    DLMF:14.20.E7
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
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    conical function
    Defining formula
    𝖰 ^ - 1 2 + i ⁢ τ - μ ⁡ ( x ) Ferrers-conical-legendre-Q-hat 𝜇 1 2 𝑖 𝜏 𝑥 {\displaystyle{\displaystyle\widehat{\mathsf{Q}}^{-\NVar{\mu}}_{\NVar{-\frac{1% }{2}+i\tau}}\left(\NVar{x}\right)}}
    xml-id
    C14.S20.E2.m2agdec
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    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2amdec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1ndec
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