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DLMF:13.2.E20 - MaRDI portal

DLMF:13.2.E20 (Q5007)

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DLMF:13.2.E20
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    Statements

    DLMF defining formula
    U ⁡ ( a , b , z ) = Γ ⁡ ( 1 - b ) Γ ⁡ ( a - b + 1 ) + O ⁡ ( z 1 - ℜ ⁡ b ) , Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 Euler-Gamma 1 𝑏 Euler-Gamma 𝑎 𝑏 1 Big-O superscript 𝑧 1 𝑏 {\displaystyle{\displaystyle U\left(a,b,z\right)=\frac{\Gamma\left(1-b\right)}% {\Gamma\left(a-b+1\right)}+O\left(z^{1-\Re b}\right),}}
    0 references
    constraint
    0 < ℜ ⁡ b < 1 0 𝑏 1 {\displaystyle{\displaystyle 0<\Re b<1}}
    0 references
    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.m2agdec
    0 references
    gamma function
    DLMF defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aidec
    0 references
    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.m2amdec
    0 references
    real part
    DLMF defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1sdec
    0 references

    Identifiers

     
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