DLMF:2.9.E8 (Q981): Difference between revisions

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Property / constraint
 

n → ∞ → 𝑛 {\displaystyle{\displaystyle n\to\infty}}

n\to\infty
Property / constraint: n → ∞ → 𝑛 {\displaystyle{\displaystyle n\to\infty}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
Defining formula:

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

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11aadec
Property / Symbols used
 
Property / Symbols used: Q11095 / rank
 
Normal rank
Property / Symbols used: Q11095 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11095 / qualifier
 
xml-id: C2.S9.XMD3.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11098 / rank
 
Normal rank
Property / Symbols used: Q11098 / qualifier
 
Defining formula:

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

a_{s,j}
Property / Symbols used: Q11098 / qualifier
 
xml-id: C2.S9.XMD7.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11099 / rank
 
Normal rank
Property / Symbols used: Q11099 / qualifier
 
Defining formula:

ρ j subscript 𝜌 𝑗 {\displaystyle{\displaystyle\rho_{j}}}

\rho_{j}
Property / Symbols used: Q11099 / qualifier
 
xml-id: C2.S9.XMD8.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11102 / rank
 
Normal rank
Property / Symbols used: Q11102 / qualifier
 
Defining formula:

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.m1dec

Latest revision as of 17:31, 1 January 2020

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DLMF:2.9.E8
No description defined

    Statements

    Defining formula
    w j ⁢ ( n ) ∼ ρ j n ⁢ n α j ⁢ ∑ s = 0 ∞ a s , j n s , asymptotic-expansion subscript 𝑤 𝑗 𝑛 superscript subscript 𝜌 𝑗 𝑛 superscript 𝑛 subscript 𝛼 𝑗 superscript subscript 𝑠 0 subscript 𝑎 𝑠 𝑗 superscript 𝑛 𝑠 {\displaystyle{\displaystyle w_{j}(n)\sim\rho_{j}^{n}n^{\alpha_{j}}\sum_{s=0}^% {\infty}\frac{a_{s,j}}{n^{s}},}}
    0 references
    DLMF id
    DLMF:2.9.E8
    0 references
    constraint
    n → ∞ → 𝑛 {\displaystyle{\displaystyle n\to\infty}}
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aadec
    0 references
    Q11095
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S9.XMD3.m1ddec
    0 references
    Q11098
    Defining formula
    a s , j subscript 𝑎 𝑠 𝑗 {\displaystyle{\displaystyle a_{s,j}}}
    xml-id
    C2.S9.XMD7.m1bdec
    0 references
    Q11099
    Defining formula
    ρ j subscript 𝜌 𝑗 {\displaystyle{\displaystyle\rho_{j}}}
    xml-id
    C2.S9.XMD8.m1cdec
    0 references
    Q11102
    Defining formula
    w j ⁢ ( n ) subscript 𝑤 𝑗 𝑛 {\displaystyle{\displaystyle w_{j}(n)}}
    xml-id
    C2.S9.XMD9.m1dec
    0 references
     
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