DLMF:9.13.E27 (Q2991): Difference between revisions

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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.m2aadec
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.m1abdec
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.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.m3abdec
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.m1pdec
Property / Symbols used
 
Property / Symbols used: index (locally) / rank
 
Normal rank
Property / Symbols used: index (locally) / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: index (locally) / qualifier
 
xml-id: C9.S13.XMD13.m1adec
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.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11425 / rank
 
Normal rank
Property / Symbols used: Q11425 / qualifier
 
test:

ℐ ℐ {\displaystyle{\displaystyle\mathscr{I}}}

\mathscr{I}
Property / Symbols used: Q11425 / qualifier
 
xml-id: C9.S13.XMD16.m1dec

Latest revision as of 14:03, 2 January 2020

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DLMF:9.13.E27
No description defined

    Statements

    test
    B k ⁡ ( z , p ) = ∫ ℐ k t - p ⁢ exp ⁡ ( z ⁢ t - 1 3 ⁢ t 3 ) ⁢ d t , Integral-generalized-Airy-B 𝑘 𝑧 𝑝 subscript subscript ℐ 𝑘 superscript 𝑡 𝑝 𝑧 𝑡 1 3 superscript 𝑡 3 𝑡 {\displaystyle{\displaystyle B_{k}\left(z,p\right)=\int_{\mathscr{I}_{k}}t^{-p% }\exp\left(zt-\tfrac{1}{3}t^{3}\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:9.13.E27
    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.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    exponential function
    test
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2abdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    Q11381
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1pdec
    0 references
    index (locally)
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C9.S13.XMD13.m1adec
    0 references
    parameter (locally)
    test
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C9.S13.XMD14.m1bdec
    0 references
    Q11425
    test
    ℐ ℐ {\displaystyle{\displaystyle\mathscr{I}}}
    xml-id
    C9.S13.XMD16.m1dec
    0 references
     
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