DLMF:9.13.E25 (Q2989): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(12 intermediate revisions by the same user not shown)
Property / constraint
 

p ∈ ℂ 𝑝 {\displaystyle{\displaystyle p\in\mathbb{C}}}

p\in\Complexes
Property / constraint: p ∈ ℂ 𝑝 {\displaystyle{\displaystyle p\in\mathbb{C}}} / rank
 
Normal rank
Property / constraint
 

k = 1 , 2 , 3 𝑘 1 2 3 {\displaystyle{\displaystyle k=1,2,3}}

k=1,2,3
Property / constraint: k = 1 , 2 , 3 𝑘 1 2 3 {\displaystyle{\displaystyle k=1,2,3}} / rank
 
Normal rank
Property / constraint
 

p ∈ ℂ 𝑝 ℂ {\displaystyle{\displaystyle p\in\mathbb{C}}}

p\in\mathbb{C}
Property / constraint: p ∈ ℂ 𝑝 ℂ {\displaystyle{\displaystyle p\in\mathbb{C}}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q11422 / rank
 
Normal rank
Property / Symbols used: Q11422 / qualifier
 
test:

A k ⁡ ( z , p ) Integral-generalized-Airy-A 𝑘 𝑧 𝑝 {\displaystyle{\displaystyle A_{\NVar{k}}\left(\NVar{z},\NVar{p}\right)}}

\genAiryintA{\NVar{k}}@{\NVar{z}}{\NVar{p}}
Property / Symbols used: Q11422 / qualifier
 
xml-id: C9.S13.SS2.p1.m1adec
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.m2akdec
Property / Symbols used
 
Property / Symbols used: Q10923 / rank
 
Normal rank
Property / Symbols used: Q10923 / qualifier
 
test:

ℂ {\displaystyle{\displaystyle\mathbb{C}}}

\Complexes
Property / Symbols used: Q10923 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r1.m2adec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1adec
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
test:

∈ {\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2adec
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.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.m3adec
Property / Symbols used
 
Property / Symbols used: Q11381 / rank
 
Normal rank
Property / Symbols used: Q11381 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11381 / qualifier
 
xml-id: C9.S1.XMD3.m1ndec
Property / Symbols used
 
Property / Symbols used: Q11423 / rank
 
Normal rank
Property / Symbols used: Q11423 / qualifier
 
test:

ℒ ℒ {\displaystyle{\displaystyle\mathscr{L}}}

\mathscr{L}
Property / Symbols used: Q11423 / qualifier
 
xml-id: C9.S13.XMD15.m1dec

Latest revision as of 14:03, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:9.13.E25
No description defined

    Statements

    test
    A k ⁡ ( z , p ) = 1 2 ⁢ π ⁢ i ⁢ ∫ ℒ k t - p ⁢ exp ⁡ ( z ⁢ t - 1 3 ⁢ t 3 ) ⁢ d t , Integral-generalized-Airy-A 𝑘 𝑧 𝑝 1 2 𝜋 𝑖 subscript subscript ℒ 𝑘 superscript 𝑡 𝑝 𝑧 𝑡 1 3 superscript 𝑡 3 𝑡 {\displaystyle{\displaystyle A_{k}\left(z,p\right)=\frac{1}{2\pi i}\int_{% \mathscr{L}_{k}}t^{-p}\exp\left(zt-\tfrac{1}{3}t^{3}\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:9.13.E25
    0 references
    constraint
    p ∈ ℂ 𝑝 {\displaystyle{\displaystyle p\in\mathbb{C}}}
    0 references
    k = 1 , 2 , 3 𝑘 1 2 3 {\displaystyle{\displaystyle k=1,2,3}}
    0 references
    p ∈ ℂ 𝑝 ℂ {\displaystyle{\displaystyle p\in\mathbb{C}}}
    0 references
    Symbols used
    Q11422
    test
    A k ⁡ ( z , p ) Integral-generalized-Airy-A 𝑘 𝑧 𝑝 {\displaystyle{\displaystyle A_{\NVar{k}}\left(\NVar{z},\NVar{p}\right)}}
    xml-id
    C9.S13.SS2.p1.m1adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2akdec
    0 references
    Q10923
    test
    ℂ {\displaystyle{\displaystyle\mathbb{C}}}
    xml-id
    introduction.Sx4.p1.t1.r1.m2adec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10784
    test
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
    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.m2aadec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q11381
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1ndec
    0 references
    Q11423
    test
    ℒ ℒ {\displaystyle{\displaystyle\mathscr{L}}}
    xml-id
    C9.S13.XMD15.m1dec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q2989&oldid=15681"