DLMF:2.11.E13 (Q1038): Difference between revisions

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Property / constraint
 

ρ → ∞ → 𝜌 {\displaystyle{\displaystyle\rho\to\infty}}

\rho\to\infty
Property / constraint: ρ → ∞ → 𝜌 {\displaystyle{\displaystyle\rho\to\infty}} / rank
 
Normal rank
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.m11addec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2afdec
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.m2afdec
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.m2abdec
Property / Symbols used
 
Property / Symbols used: terminant function / rank
 
Normal rank
Property / Symbols used: terminant function / qualifier
 
test:

F p ⁡ ( z ) terminant-function 𝑝 𝑧 {\displaystyle{\displaystyle F_{\NVar{p}}\left(\NVar{z}\right)}}

\terminant{\NVar{p}}@{\NVar{z}}
Property / Symbols used: terminant function / qualifier
 
xml-id: C2.S11.E11.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11136 / rank
 
Normal rank
Property / Symbols used: Q11136 / qualifier
 
test:

ρ 𝜌 {\displaystyle{\displaystyle\rho}}

\rho
Property / Symbols used: Q11136 / qualifier
 
xml-id: C2.S11.XMD3.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11137 / rank
 
Normal rank
Property / Symbols used: Q11137 / qualifier
 
test:

θ 𝜃 {\displaystyle{\displaystyle\theta}}

\theta
Property / Symbols used: Q11137 / qualifier
 
xml-id: C2.S11.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: Q11138 / rank
 
Normal rank
Property / Symbols used: Q11138 / qualifier
 
test:

a 2 ⁢ s ⁢ ( θ , α ) subscript 𝑎 2 𝑠 𝜃 𝛼 {\displaystyle{\displaystyle a_{2s}(\theta,\alpha)}}

a_{2s}(\theta,\alpha)
Property / Symbols used: Q11138 / qualifier
 
xml-id: C2.S11.XMD6.m1dec

Latest revision as of 16:40, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:2.11.E13
No description defined

    Statements

    test
    F n + p ⁡ ( z ) ∼ e - i ⁢ ( ρ + α ) ⁢ θ 1 + e - i ⁢ θ ⁢ e - ρ - z ( 2 ⁢ π ⁢ ρ ) 1 / 2 ⁢ ∑ s = 0 ∞ a 2 ⁢ s ⁢ ( θ , α ) ρ s , asymptotic-expansion terminant-function 𝑛 𝑝 𝑧 superscript 𝑒 𝑖 𝜌 𝛼 𝜃 1 superscript 𝑒 𝑖 𝜃 superscript 𝑒 𝜌 𝑧 superscript 2 𝜋 𝜌 1 2 superscript subscript 𝑠 0 subscript 𝑎 2 𝑠 𝜃 𝛼 superscript 𝜌 𝑠 {\displaystyle{\displaystyle F_{n+p}\left(z\right)\sim\frac{e^{-i(\rho+\alpha)% \theta}}{1+e^{-i\theta}}\frac{e^{-\rho-z}}{(2\pi\rho)^{1/2}}\sum_{s=0}^{\infty% }\frac{a_{2s}(\theta,\alpha)}{\rho^{s}},}}
    0 references
    DLMF id
    DLMF:2.11.E13
    0 references
    constraint
    ρ → ∞ → 𝜌 {\displaystyle{\displaystyle\rho\to\infty}}
    0 references
    Symbols used
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11addec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    terminant function
    test
    F p ⁡ ( z ) terminant-function 𝑝 𝑧 {\displaystyle{\displaystyle F_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C2.S11.E11.m2acdec
    0 references
    Q11136
    test
    ρ 𝜌 {\displaystyle{\displaystyle\rho}}
    xml-id
    C2.S11.XMD3.m1bdec
    0 references
    Q11137
    test
    θ 𝜃 {\displaystyle{\displaystyle\theta}}
    xml-id
    C2.S11.XMD4.m1adec
    0 references
    Q11138
    test
    a 2 ⁢ s ⁢ ( θ , α ) subscript 𝑎 2 𝑠 𝜃 𝛼 {\displaystyle{\displaystyle a_{2s}(\theta,\alpha)}}
    xml-id
    C2.S11.XMD6.m1dec
    0 references
     
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