DLMF:2.7.E12 (Q903): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
test:

∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11adec
Property / Symbols used
 
Property / Symbols used: Q11054 / rank
 
Normal rank
Property / Symbols used: Q11054 / qualifier
 
test:

a s , j subscript 𝑎 𝑠 𝑗 {\displaystyle{\displaystyle a_{s,j}}}

a_{s,j}
Property / Symbols used: Q11054 / qualifier
 
xml-id: C2.S7.XMD13.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11055 / rank
 
Normal rank
Property / Symbols used: Q11055 / qualifier
 
test:

λ j subscript 𝜆 𝑗 {\displaystyle{\displaystyle\lambda_{j}}}

\lambda_{j}
Property / Symbols used: Q11055 / qualifier
 
xml-id: C2.S7.XMD14.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11056 / rank
 
Normal rank
Property / Symbols used: Q11056 / qualifier
 
test:

μ j subscript 𝜇 𝑗 {\displaystyle{\displaystyle\mu_{j}}}

\mu_{j}
Property / Symbols used: Q11056 / qualifier
 
xml-id: C2.S7.XMD15.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11057 / rank
 
Normal rank
Property / Symbols used: Q11057 / qualifier
 
test:

Λ j subscript Λ 𝑗 {\displaystyle{\displaystyle\Lambda_{j}}}

\Lambda_{j}
Property / Symbols used: Q11057 / qualifier
 
xml-id: C2.S7.XMD16.m1dec

Latest revision as of 16:21, 1 January 2020

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DLMF:2.7.E12
No description defined

    Statements

    test
    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
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
    0 references
    Q11054
    test
    a s , j subscript 𝑎 𝑠 𝑗 {\displaystyle{\displaystyle a_{s,j}}}
    xml-id
    C2.S7.XMD13.m1bdec
    0 references
    Q11055
    test
    λ j subscript 𝜆 𝑗 {\displaystyle{\displaystyle\lambda_{j}}}
    xml-id
    C2.S7.XMD14.m1cdec
    0 references
    Q11056
    test
    μ j subscript 𝜇 𝑗 {\displaystyle{\displaystyle\mu_{j}}}
    xml-id
    C2.S7.XMD15.m1cdec
    0 references
    Q11057
    test
    Λ j subscript Λ 𝑗 {\displaystyle{\displaystyle\Lambda_{j}}}
    xml-id
    C2.S7.XMD16.m1dec
    0 references
     
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