DLMF:36.2.E21 (Q9863): Difference between revisions

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Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q10919 / rank
 
Normal rank
Property / Symbols used: Q10919 / qualifier
 
Defining formula:

Ai ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}

\AiryAi@{\NVar{z}}
Property / Symbols used: Q10919 / qualifier
 
xml-id: C9.S2.SS1.m1addec
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
 
Defining formula:

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: hyperbolic umbilic canonical integral function / rank
 
Normal rank
Property / Symbols used: hyperbolic umbilic canonical integral function / qualifier
 
Defining formula:

Ψ ( H ) ( 𝐱 ) hyperbolic-umbilic-canonical-integral 𝐱 {\displaystyle{\displaystyle\Psi^{(\mathrm{H})}\left(\NVar{\mathbf{x}}\right)}}

\hyperumbcanonint@{\NVar{\mathbf{x}}}
Property / Symbols used: hyperbolic umbilic canonical integral function / qualifier
 
xml-id: C36.S2.E5.m4addec
Property / Symbols used
 
Property / Symbols used: Q12745 / rank
 
Normal rank
Property / Symbols used: Q12745 / qualifier
 
Defining formula:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q12745 / qualifier
 
xml-id: C36.S1.XMD10.m1hdec
Property / Symbols used
 
Property / Symbols used: Q12748 / rank
 
Normal rank
Property / Symbols used: Q12748 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12748 / qualifier
 
xml-id: C36.S1.XMD9.m1hdec

Latest revision as of 15:06, 2 January 2020

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DLMF:36.2.E21
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    Statements

    Ψ ( H ) ( x , y , 0 ) = 4 π 2 3 2 / 3 Ai ( x 3 1 / 3 ) Ai ( y 3 1 / 3 ) . hyperbolic-umbilic-canonical-integral 𝑥 𝑦 0 4 superscript 𝜋 2 superscript 3 2 3 Airy-Ai 𝑥 superscript 3 1 3 Airy-Ai 𝑦 superscript 3 1 3 {\displaystyle{\displaystyle\Psi^{(\mathrm{H})}\left(x,y,0\right)=\frac{4\pi^{% 2}}{3^{2/3}}\mathrm{Ai}\left(\frac{x}{3^{1/3}}\right)\mathrm{Ai}\left(\frac{y}% {3^{1/3}}\right).}}
    0 references
    DLMF:36.2.E21
    0 references
    Ai ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    C9.S2.SS1.m1addec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2akdec
    0 references
    Ψ ( H ) ( 𝐱 ) hyperbolic-umbilic-canonical-integral 𝐱 {\displaystyle{\displaystyle\Psi^{(\mathrm{H})}\left(\NVar{\mathbf{x}}\right)}}
    C36.S2.E5.m4addec
    0 references
    y 𝑦 {\displaystyle{\displaystyle y}}
    C36.S1.XMD10.m1hdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C36.S1.XMD9.m1hdec
    0 references