DLMF:9.13.E26 (Q2990): Difference between revisions

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Property / constraint
 

p = 0 , ± 1 , ± 2 , … 𝑝 0 plus-or-minus 1 plus-or-minus 2 … {\displaystyle{\displaystyle p=0,\pm 1,\pm 2,\ldots}}

p=0,\pm 1,\pm 2,\ldots
Property / constraint: p = 0 , ± 1 , ± 2 , … 𝑝 0 plus-or-minus 1 plus-or-minus 2 … {\displaystyle{\displaystyle p=0,\pm 1,\pm 2,\ldots}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q11424 / rank
 
Normal rank
Property / Symbols used: Q11424 / qualifier
 
test:

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

\genAiryintB{\NVar{k}}@{\NVar{z}}{\NVar{p}}
Property / Symbols used: Q11424 / qualifier
 
xml-id: C9.S13.SS2.p1.m2adec
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.m2aldec
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.m1aadec
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.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.m2abdec
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.m3aadec
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.m1odec
Property / Symbols used
 
Property / Symbols used: parameter (locally) / rank
 
Normal rank
Property / Symbols used: parameter (locally) / qualifier
 
test:

p 𝑝 {\displaystyle{\displaystyle p}}

p
Property / Symbols used: parameter (locally) / qualifier
 
xml-id: C9.S13.XMD14.m1adec
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.m1adec

Latest revision as of 14:03, 2 January 2020

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DLMF:9.13.E26
No description defined

    Statements

    test
    B 0 ⁡ ( z , p ) = 1 2 ⁢ π ⁢ i ⁢ ∫ ℒ 0 t - p ⁢ exp ⁡ ( z ⁢ t - 1 3 ⁢ t 3 ) ⁢ d t , Integral-generalized-Airy-B 0 𝑧 𝑝 1 2 𝜋 𝑖 subscript subscript ℒ 0 superscript 𝑡 𝑝 𝑧 𝑡 1 3 superscript 𝑡 3 𝑡 {\displaystyle{\displaystyle B_{0}\left(z,p\right)=\frac{1}{2\pi i}\int_{% \mathscr{L}_{0}}t^{-p}\exp\left(zt-\tfrac{1}{3}t^{3}\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:9.13.E26
    0 references
    constraint
    p = 0 , ± 1 , ± 2 , … 𝑝 0 plus-or-minus 1 plus-or-minus 2 … {\displaystyle{\displaystyle p=0,\pm 1,\pm 2,\ldots}}
    0 references
    Symbols used
    Q11424
    test
    B k ⁡ ( z , p ) Integral-generalized-Airy-B 𝑘 𝑧 𝑝 {\displaystyle{\displaystyle B_{\NVar{k}}\left(\NVar{z},\NVar{p}\right)}}
    xml-id
    C9.S13.SS2.p1.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aldec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    exponential function
    test
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2aadec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q11381
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1odec
    0 references
    parameter (locally)
    test
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C9.S13.XMD14.m1adec
    0 references
    Q11423
    test
    ℒ ℒ {\displaystyle{\displaystyle\mathscr{L}}}
    xml-id
    C9.S13.XMD15.m1adec
    0 references
     
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