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DLMF:5.11.E13 - MaRDI portal

DLMF:5.11.E13 (Q2833)

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DLMF:5.11.E13
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    Statements

    DLMF defining formula
    Γ ⁡ ( z + a ) Γ ⁡ ( z + b ) ∼ z a - b ⁢ ∑ k = 0 ∞ G k ⁢ ( a , b ) z k , asymptotic-expansion Euler-Gamma 𝑧 𝑎 Euler-Gamma 𝑧 𝑏 superscript 𝑧 𝑎 𝑏 superscript subscript 𝑘 0 subscript 𝐺 𝑘 𝑎 𝑏 superscript 𝑧 𝑘 {\displaystyle{\displaystyle\frac{\Gamma\left(z+a\right)}{\Gamma\left(z+b% \right)}\sim z^{a-b}\sum_{k=0}^{\infty}\frac{G_{k}(a,b)}{z^{k}},}}
    0 references
    Symbols used
    gamma function
    DLMF defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2ahdec
    0 references
    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11addec
    0 references
    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C5.S1.XMD4.m1gdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C5.S1.XMD7.m1hdec
    0 references
    real or complex variable
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C5.S1.XMD8.m1adec
    0 references
    real or complex variable
    DLMF defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C5.S1.XMD9.m1bdec
    0 references
    coefficients (locally)
    DLMF defining formula
    G k ⁢ ( a , b ) subscript 𝐺 𝑘 𝑎 𝑏 {\displaystyle{\displaystyle G_{k}(a,b)}}
    xml-id
    C5.S11.XMD4.m1dec
    0 references

    Identifiers

     
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