DLMF:2.7.E12 (Q903)

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DLMF:2.7.E12
No description defined

    Statements

    Defining formula
    a s , 1 ∼ Λ 1 ( λ 1 - λ 2 ) s ⁢ ∑ j = 0 ∞ a j , 2 ⁢ ( λ 1 - λ 2 ) j ⁢ Γ ⁡ ( s + μ 2 - μ 1 - j ) , asymptotic-expansion subscript 𝑎 𝑠 1 subscript Λ 1 superscript subscript 𝜆 1 subscript 𝜆 2 𝑠 superscript subscript 𝑗 0 subscript 𝑎 𝑗 2 superscript subscript 𝜆 1 subscript 𝜆 2 𝑗 Euler-Gamma 𝑠 subscript 𝜇 2 subscript 𝜇 1 𝑗 {\displaystyle{\displaystyle a_{s,1}\sim\frac{\Lambda_{1}}{(\lambda_{1}-% \lambda_{2})^{s}}\*\sum_{j=0}^{\infty}{a_{j,2}(\lambda_{1}-\lambda_{2})^{j}% \Gamma\left(s+\mu_{2}-\mu_{1}-j\right)},}}
    0 references
    DLMF id
    DLMF:2.7.E12
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
    0 references
    Q11054
    Defining formula
    a s , j subscript 𝑎 𝑠 𝑗 {\displaystyle{\displaystyle a_{s,j}}}
    xml-id
    C2.S7.XMD13.m1bdec
    0 references
    Q11055
    Defining formula
    λ j subscript 𝜆 𝑗 {\displaystyle{\displaystyle\lambda_{j}}}
    xml-id
    C2.S7.XMD14.m1cdec
    0 references
    Q11056
    Defining formula
    μ j subscript 𝜇 𝑗 {\displaystyle{\displaystyle\mu_{j}}}
    xml-id
    C2.S7.XMD15.m1cdec
    0 references
    Q11057
    Defining formula
    Λ j subscript Λ 𝑗 {\displaystyle{\displaystyle\Lambda_{j}}}
    xml-id
    C2.S7.XMD16.m1dec
    0 references
     
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