DLMF:2.6.E31 (Q857): 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
 
test:

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: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q11024 / rank
 
Normal rank
Property / Symbols used: Q11024 / qualifier
 
test:

c ≠ 0 𝑐 0 {\displaystyle{\displaystyle c\neq 0}}

c\neq 0
Property / Symbols used: Q11024 / qualifier
 
xml-id: C2.S6.XMD13.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11019 / rank
 
Normal rank
Property / Symbols used: Q11019 / qualifier
 
test:

f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}

f(t)
Property / Symbols used: Q11019 / qualifier
 
xml-id: C2.S6.XMD2.m1ldec
Property / Symbols used
 
Property / Symbols used: Q11020 / rank
 
Normal rank
Property / Symbols used: Q11020 / qualifier
 
test:

a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}

a_{n}
Property / Symbols used: Q11020 / qualifier
 
xml-id: C2.S6.XMD3.m1hdec

Latest revision as of 16:14, 1 January 2020

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DLMF:2.6.E31
No description defined

    Statements

    test
    f ⁢ ( t ) ∼ e i ⁢ c ⁢ t ⁢ ∑ s = 0 ∞ a s ⁢ t - s - α , asymptotic-expansion 𝑓 𝑡 superscript 𝑒 𝑖 𝑐 𝑡 superscript subscript 𝑠 0 subscript 𝑎 𝑠 superscript 𝑡 𝑠 𝛼 {\displaystyle{\displaystyle f(t)\sim e^{ict}\sum_{s=0}^{\infty}a_{s}t^{-s-% \alpha},}}
    0 references
    DLMF id
    DLMF:2.6.E31
    0 references
    constraint
    t → + ∞ → 𝑡 {\displaystyle{\displaystyle t\to+\infty}}
    0 references
    Symbols used
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11acdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q11024
    test
    c ≠ 0 𝑐 0 {\displaystyle{\displaystyle c\neq 0}}
    xml-id
    C2.S6.XMD13.m1cdec
    0 references
    Q11019
    test
    f ⁢ ( t ) 𝑓 𝑡 {\displaystyle{\displaystyle f(t)}}
    xml-id
    C2.S6.XMD2.m1ldec
    0 references
    Q11020
    test
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C2.S6.XMD3.m1hdec
    0 references
     
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