DLMF:2.9.E13 (Q986): Difference between revisions

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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.m11addec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q11103 / rank
 
Normal rank
Property / Symbols used: Q11103 / qualifier
 
test:

ρ 𝜌 {\displaystyle{\displaystyle\rho}}

\rho
Property / Symbols used: Q11103 / qualifier
 
xml-id: C2.S9.XMD10.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11106 / rank
 
Normal rank
Property / Symbols used: Q11106 / qualifier
 
test:

b s subscript 𝑏 𝑠 {\displaystyle{\displaystyle b_{s}}}

b_{s}
Property / Symbols used: Q11106 / qualifier
 
xml-id: C2.S9.XMD13.m1dec
Property / Symbols used
 
Property / Symbols used: Q11105 / rank
 
Normal rank
Property / Symbols used: Q11105 / qualifier
 
test:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q11105 / qualifier
 
xml-id: C2.S9.XMD14.m1adec
Property / Symbols used
 
Property / Symbols used: Q11102 / rank
 
Normal rank
Property / Symbols used: Q11102 / qualifier
 
test:

w j ⁢ ( n ) subscript 𝑤 𝑗 𝑛 {\displaystyle{\displaystyle w_{j}(n)}}

w_{j}(n)
Property / Symbols used: Q11102 / qualifier
 
xml-id: C2.S9.XMD9.m1cdec

Latest revision as of 16:32, 1 January 2020

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DLMF:2.9.E13
No description defined

    Statements

    test
    w 2 ⁢ ( n ) ∼ ρ n ⁢ n α 2 ⁢ ∑ s = 0 s ≠ α 2 - α 1 ∞ b s n s + c ⁢ w 1 ⁢ ( n ) ⁢ ln ⁡ n , asymptotic-expansion subscript 𝑤 2 𝑛 superscript 𝜌 𝑛 superscript 𝑛 subscript 𝛼 2 superscript subscript 𝑠 0 𝑠 subscript 𝛼 2 subscript 𝛼 1 subscript 𝑏 𝑠 superscript 𝑛 𝑠 𝑐 subscript 𝑤 1 𝑛 𝑛 {\displaystyle{\displaystyle w_{2}(n)\sim\rho^{n}n^{\alpha_{2}}\sum_{% \begin{subarray}{c}s=0\\ s\neq\alpha_{2}-\alpha_{1}\end{subarray}}^{\infty}\frac{b_{s}}{n^{s}}+cw_{1}(n% )\ln n,}}
    0 references
    DLMF id
    DLMF:2.9.E13
    0 references
    constraint
    n → ∞ → 𝑛 {\displaystyle{\displaystyle n\to\infty}}
    0 references
    Symbols used
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11addec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    Q11103
    test
    ρ 𝜌 {\displaystyle{\displaystyle\rho}}
    xml-id
    C2.S9.XMD10.m1bdec
    0 references
    Q11106
    test
    b s subscript 𝑏 𝑠 {\displaystyle{\displaystyle b_{s}}}
    xml-id
    C2.S9.XMD13.m1dec
    0 references
    Q11105
    test
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C2.S9.XMD14.m1adec
    0 references
    Q11102
    test
    w j ⁢ ( n ) subscript 𝑤 𝑗 𝑛 {\displaystyle{\displaystyle w_{j}(n)}}
    xml-id
    C2.S9.XMD9.m1cdec
    0 references
     
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