DLMF:2.11.E12 (Q1037): Difference between revisions

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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.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3acdec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2adec
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.m2abdec
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.m1adec
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.m1dec

Latest revision as of 16:40, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:2.11.E12
No description defined

    Statements

    test
    F n + p ⁡ ( z ) = e - z 2 ⁢ π ⁢ ∫ 0 ∞ exp ⁡ ( - ρ ⁢ ( t ⁢ e i ⁢ θ - ln ⁡ t ) ) ⁢ t α - 1 1 + t ⁢ d t . terminant-function 𝑛 𝑝 𝑧 superscript 𝑒 𝑧 2 𝜋 superscript subscript 0 𝜌 𝑡 superscript 𝑒 𝑖 𝜃 𝑡 superscript 𝑡 𝛼 1 1 𝑡 𝑡 {\displaystyle{\displaystyle F_{n+p}\left(z\right)=\frac{e^{-z}}{2\pi}\int_{0}% ^{\infty}\exp\left(-\rho\left(te^{i\theta}-\ln t\right)\right)\frac{t^{\alpha-% 1}}{1+t}\mathrm{d}t.}}
    0 references
    DLMF id
    DLMF:2.11.E12
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    exponential function
    test
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    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.m2abdec
    0 references
    Q11136
    test
    ρ 𝜌 {\displaystyle{\displaystyle\rho}}
    xml-id
    C2.S11.XMD3.m1adec
    0 references
    Q11137
    test
    θ 𝜃 {\displaystyle{\displaystyle\theta}}
    xml-id
    C2.S11.XMD4.m1dec
    0 references
     
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