DLMF:13.2.E17 (Q4307)

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DLMF:13.2.E17
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    Statements

    Defining formula
    U ⁡ ( a , 2 , z ) = 1 Γ ⁡ ( a ) ⁢ z - 1 + O ⁡ ( ln ⁡ z ) , Kummer-confluent-hypergeometric-U 𝑎 2 𝑧 1 Euler-Gamma 𝑎 superscript 𝑧 1 Big-O 𝑧 {\displaystyle{\displaystyle U\left(a,2,z\right)=\frac{1}{\Gamma\left(a\right)% }z^{-1}+O\left(\ln z\right),}}
    0 references
    DLMF id
    DLMF:13.2.E17
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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.m2addec
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    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2afdec
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    Kummer confluent hypergeometric function
    Defining formula
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2ajdec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1pdec
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