DLMF:2.7.E14 (Q905): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11054 / rank
 
Normal rank
Property / Symbols used: Q11054 / qualifier
 
Defining formula:

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.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11055 / rank
 
Normal rank
Property / Symbols used: Q11055 / qualifier
 
Defining formula:

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

\lambda_{j}
Property / Symbols used: Q11055 / qualifier
 
xml-id: C2.S7.XMD14.m1edec
Property / Symbols used
 
Property / Symbols used: Q11056 / rank
 
Normal rank
Property / Symbols used: Q11056 / qualifier
 
Defining formula:

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

\mu_{j}
Property / Symbols used: Q11056 / qualifier
 
xml-id: C2.S7.XMD15.m1edec
Property / Symbols used
 
Property / Symbols used: Q11050 / rank
 
Normal rank
Property / Symbols used: Q11050 / qualifier
 
Defining formula:

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

w_{j}(z)
Property / Symbols used: Q11050 / qualifier
 
xml-id: C2.S7.XMD8.m1bdec

Latest revision as of 17:21, 1 January 2020

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DLMF:2.7.E14
No description defined

    Statements

    Defining formula
    w j ⁢ ( z ) ∼ e λ j ⁢ z ⁢ ( ( λ 2 - λ 1 ) ⁢ z ) μ j ⁢ ∑ s = 0 ∞ a s , j z s asymptotic-expansion subscript 𝑤 𝑗 𝑧 superscript 𝑒 subscript 𝜆 𝑗 𝑧 superscript subscript 𝜆 2 subscript 𝜆 1 𝑧 subscript 𝜇 𝑗 superscript subscript 𝑠 0 subscript 𝑎 𝑠 𝑗 superscript 𝑧 𝑠 {\displaystyle{\displaystyle w_{j}(z)\sim e^{\lambda_{j}z}((\lambda_{2}-% \lambda_{1})z)^{\mu_{j}}\sum_{s=0}^{\infty}\frac{a_{s,j}}{z^{s}}}}
    0 references
    DLMF id
    DLMF:2.7.E14
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11abdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    Q11054
    Defining formula
    a s , j subscript 𝑎 𝑠 𝑗 {\displaystyle{\displaystyle a_{s,j}}}
    xml-id
    C2.S7.XMD13.m1ddec
    0 references
    Q11055
    Defining formula
    λ j subscript 𝜆 𝑗 {\displaystyle{\displaystyle\lambda_{j}}}
    xml-id
    C2.S7.XMD14.m1edec
    0 references
    Q11056
    Defining formula
    μ j subscript 𝜇 𝑗 {\displaystyle{\displaystyle\mu_{j}}}
    xml-id
    C2.S7.XMD15.m1edec
    0 references
    Q11050
    Defining formula
    w j ⁢ ( z ) subscript 𝑤 𝑗 𝑧 {\displaystyle{\displaystyle w_{j}(z)}}
    xml-id
    C2.S7.XMD8.m1bdec
    0 references
     
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