DLMF:14.15.E3 (Q4849)

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DLMF:14.15.E3
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    Statements

    Defining formula
    𝑸 ν μ ⁡ ( x ) = 1 μ ν + ( 1 / 2 ) ⁢ ( π ⁢ u 2 ) 1 / 2 ⁢ I ν + 1 2 ⁡ ( μ ⁢ u ) ⁢ ( 1 + O ⁡ ( 1 μ ) ) , associated-Legendre-black-Q 𝜇 𝜈 𝑥 1 superscript 𝜇 𝜈 1 2 superscript 𝜋 𝑢 2 1 2 modified-Bessel-first-kind 𝜈 1 2 𝜇 𝑢 1 Big-O 1 𝜇 {\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu}\left(x\right)=\frac{1}{% \mu^{\nu+(1/2)}}\left(\frac{\pi u}{2}\right)^{1/2}I_{\nu+\frac{1}{2}}\left(\mu u% \right)\left(1+O\left(\frac{1}{\mu}\right)\right),}}
    0 references
    DLMF id
    DLMF:14.15.E3
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    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2abdec
    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.m3adec
    0 references
     
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