DLMF:8.18.E3 (Q2669)

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DLMF:8.18.E3
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    Statements

    Defining formula
    I x ⁡ ( a , b ) = Γ ⁡ ( a + b ) Γ ⁡ ( a ) ⁢ ( ∑ k = 0 n - 1 d k ⁢ F k + O ⁡ ( a - n ) ⁢ F 0 ) , IncI 𝑥 𝑎 𝑏 Euler-Gamma 𝑎 𝑏 Euler-Gamma 𝑎 superscript subscript 𝑘 0 𝑛 1 subscript 𝑑 𝑘 subscript 𝐹 𝑘 Big-O superscript 𝑎 𝑛 subscript 𝐹 0 {\displaystyle{\displaystyle I_{x}\left(a,b\right)=\frac{\Gamma\left(a+b\right% )}{\Gamma\left(a\right)}\left(\sum_{k=0}^{n-1}d_{k}F_{k}+O\left(a^{-n}\right)F% _{0}\right),}}
    0 references
    DLMF id
    DLMF:8.18.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.m2aadec
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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.m2aadec
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    incomplete beta function
    Defining formula
    I x ⁡ ( a , b ) IncI 𝑥 𝑎 𝑏 {\displaystyle{\displaystyle I_{\NVar{x}}\left(\NVar{a},\NVar{b}\right)}}
    xml-id
    C8.S17.E2.m2aadec
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