DLMF:2.5.E18 (Q794): 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.m11aadec
Property / Symbols used
 
Property / Symbols used: exponential function / rank
 
Normal rank
Property / Symbols used: exponential function / qualifier
 
test:

exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}

\exp@@{\NVar{z}}
Property / Symbols used: exponential function / qualifier
 
xml-id: C4.S2.E19.m2adec
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.m2addec
Property / Symbols used
 
Property / Symbols used: Q11005 / rank
 
Normal rank
Property / Symbols used: Q11005 / qualifier
 
test:

h ⁢ ( x ) ℎ 𝑥 {\displaystyle{\displaystyle h(x)}}

h(x)
Property / Symbols used: Q11005 / qualifier
 
xml-id: C2.S5.XMD16.m1dec
Property / Symbols used
 
Property / Symbols used: Q11006 / rank
 
Normal rank
Property / Symbols used: Q11006 / qualifier
 
test:

κ 𝜅 {\displaystyle{\displaystyle\kappa}}

\kappa
Property / Symbols used: Q11006 / qualifier
 
xml-id: C2.S5.XMD17.m1dec
Property / Symbols used
 
Property / Symbols used: Q11007 / rank
 
Normal rank
Property / Symbols used: Q11007 / qualifier
 
test:

p 𝑝 {\displaystyle{\displaystyle p}}

p
Property / Symbols used: Q11007 / qualifier
 
xml-id: C2.S5.XMD18.m1dec
Property / Symbols used
 
Property / Symbols used: Q11008 / rank
 
Normal rank
Property / Symbols used: Q11008 / qualifier
 
test:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q11008 / qualifier
 
xml-id: C2.S5.XMD3.m1dec

Latest revision as of 16:04, 1 January 2020

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DLMF:2.5.E18
No description defined

    Statements

    test
    h ⁢ ( t ) ∼ exp ⁡ ( i ⁢ κ ⁢ t p ) ⁢ ∑ s = 0 ∞ b s ⁢ t - β s , asymptotic-expansion ℎ 𝑡 𝑖 𝜅 superscript 𝑡 𝑝 superscript subscript 𝑠 0 subscript 𝑏 𝑠 superscript 𝑡 subscript 𝛽 𝑠 {\displaystyle{\displaystyle h(t)\sim\exp\left(i\kappa t^{p}\right)\sum_{s=0}^% {\infty}b_{s}t^{-\beta_{s}},}}
    0 references
    DLMF id
    DLMF:2.5.E18
    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.m11aadec
    0 references
    exponential function
    test
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
    0 references
    Q11005
    test
    h ⁢ ( x ) ℎ 𝑥 {\displaystyle{\displaystyle h(x)}}
    xml-id
    C2.S5.XMD16.m1dec
    0 references
    Q11006
    test
    κ 𝜅 {\displaystyle{\displaystyle\kappa}}
    xml-id
    C2.S5.XMD17.m1dec
    0 references
    Q11007
    test
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C2.S5.XMD18.m1dec
    0 references
    Q11008
    test
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C2.S5.XMD3.m1dec
    0 references
     
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