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DLMF:13.2.E16 - MaRDI portal

DLMF:13.2.E16 (Q5003)

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DLMF:13.2.E16
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    Statements

    DLMF defining formula
    U ⁡ ( a , b , z ) = Γ ⁡ ( b - 1 ) Γ ⁡ ( a ) ⁢ z 1 - b + O ⁡ ( z 2 - ℜ ⁡ b ) , Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 Euler-Gamma 𝑏 1 Euler-Gamma 𝑎 superscript 𝑧 1 𝑏 Big-O superscript 𝑧 2 𝑏 {\displaystyle{\displaystyle U\left(a,b,z\right)=\frac{\Gamma\left(b-1\right)}% {\Gamma\left(a\right)}z^{1-b}+O\left(z^{2-\Re b}\right),}}
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    constraint
    ℜ ⁡ b ≥ 2 𝑏 2 {\displaystyle{\displaystyle\Re b\geq 2}}
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    ℜ ⁡ b ≥ 2 𝑏 2 {\displaystyle{\displaystyle\Re b\geq 2}}
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    b ≠ 2 𝑏 2 {\displaystyle{\displaystyle b\not=2}}
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    Symbols used
    order not exceeding
    DLMF defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2acdec
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    gamma function
    DLMF defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aedec
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    Kummer confluent hypergeometric function
    DLMF 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.m2aidec
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    real part
    DLMF defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1odec
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    Identifiers

     
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