DLMF:2.8.E11 (Q945): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11076 / rank
 
Normal rank
Property / Symbols used: Q11076 / qualifier
 
test:

𝚫 j ⁢ ( α j ) subscript 𝚫 𝑗 subscript 𝛼 𝑗 {\displaystyle{\displaystyle\mathbf{\Delta}_{j}(\alpha_{j})}}

\mathbf{\Delta}_{j}(\alpha_{j})
Property / Symbols used: Q11076 / qualifier
 
xml-id: C2.S8.XMD13.m1dec
Property / Symbols used
 
Property / Symbols used: Q11069 / rank
 
Normal rank
Property / Symbols used: Q11069 / qualifier
 
test:

u 𝑢 {\displaystyle{\displaystyle u}}

u
Property / Symbols used: Q11069 / qualifier
 
xml-id: C2.S8.XMD4.m1edec

Latest revision as of 16:25, 1 January 2020

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DLMF:2.8.E11
No description defined

    Statements

    test
    W n , 1 ⁢ ( u , ξ ) = e u ⁢ ξ ⁢ ( ∑ s = 0 n - 1 A s ⁢ ( ξ ) u s + O ⁡ ( 1 u n ) ) , subscript 𝑊 𝑛 1 𝑢 𝜉 superscript 𝑒 𝑢 𝜉 superscript subscript 𝑠 0 𝑛 1 subscript 𝐴 𝑠 𝜉 superscript 𝑢 𝑠 Big-O 1 superscript 𝑢 𝑛 {\displaystyle{\displaystyle W_{n,1}(u,\xi)=e^{u\xi}\left(\sum_{s=0}^{n-1}% \frac{A_{s}(\xi)}{u^{s}}+O\left(\frac{1}{u^{n}}\right)\right),}}
    0 references
    DLMF id
    DLMF:2.8.E11
    0 references
    constraint
    ξ ∈ 𝚫 1 ⁢ ( α 1 ) 𝜉 subscript 𝚫 1 subscript 𝛼 1 {\displaystyle{\displaystyle\xi\in\mathbf{\Delta}_{1}(\alpha_{1})}}
    0 references
    Symbols used
    order not exceeding
    test
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
    0 references
    Q10784
    test
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q11074
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S8.XMD10.m1dec
    0 references
    Q11073
    test
    W n , j ⁢ ( u , ξ ) subscript 𝑊 𝑛 𝑗 𝑢 𝜉 {\displaystyle{\displaystyle W_{n,j}(u,\xi)}}
    xml-id
    C2.S8.XMD11.m1adec
    0 references
    Q11075
    test
    A s ⁢ ( ξ ) subscript 𝐴 𝑠 𝜉 {\displaystyle{\displaystyle A_{s}(\xi)}}
    xml-id
    C2.S8.XMD12.m1dec
    0 references
    Q11076
    test
    𝚫 j ⁢ ( α j ) subscript 𝚫 𝑗 subscript 𝛼 𝑗 {\displaystyle{\displaystyle\mathbf{\Delta}_{j}(\alpha_{j})}}
    xml-id
    C2.S8.XMD13.m1dec
    0 references
    Q11069
    test
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C2.S8.XMD4.m1edec
    0 references
     
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