DLMF:9.8.E16 (Q2850): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Airy modulus function / rank
 
Normal rank
Property / Symbols used: Airy modulus function / qualifier
 
test:

M ⁡ ( z ) modulus-Airy-M 𝑧 {\displaystyle{\displaystyle M\left(\NVar{z}\right)}}

\AirymodM@{\NVar{z}}
Property / Symbols used: Airy modulus function / qualifier
 
xml-id: C9.S8.E3.m2agdec
Property / Symbols used
 
Property / Symbols used: Airy modulus function / rank
 
Normal rank
Property / Symbols used: Airy modulus function / qualifier
 
test:

N ⁡ ( z ) modulus-Airy-N 𝑧 {\displaystyle{\displaystyle N\left(\NVar{z}\right)}}

\AirymodderivN@{\NVar{z}}
Property / Symbols used: Airy modulus function / qualifier
 
xml-id: C9.S8.E7.m2agdec
Property / Symbols used
 
Property / Symbols used: Airy phase function / rank
 
Normal rank
Property / Symbols used: Airy phase function / qualifier
 
test:

ϕ ⁡ ( z ) phase-Airy-Phi 𝑧 {\displaystyle{\displaystyle\phi\left(\NVar{z}\right)}}

\Airyphasederivphi@{\NVar{z}}
Property / Symbols used: Airy phase function / qualifier
 
xml-id: C9.S8.E8.m2afdec
Property / Symbols used
 
Property / Symbols used: Q11382 / rank
 
Normal rank
Property / Symbols used: Q11382 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11382 / qualifier
 
xml-id: C9.S1.XMD2.m1odec

Latest revision as of 14:40, 2 January 2020

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DLMF:9.8.E16
No description defined

    Statements

    test
    x 2 ⁢ M 2 ⁡ ( x ) = N ′ 2 ⁡ ( x ) + N 2 ⁡ ( x ) ⁢ ϕ ′ 2 ⁡ ( x ) = N ′ 2 ⁡ ( x ) + π - 2 ⁢ x 2 ⁢ N - 2 ⁡ ( x ) , superscript 𝑥 2 modulus-Airy-M 2 𝑥 diffop modulus-Airy-N 1 2 𝑥 modulus-Airy-N 2 𝑥 diffop phase-Airy-Phi 1 2 𝑥 diffop modulus-Airy-N 1 2 𝑥 superscript 𝜋 2 superscript 𝑥 2 modulus-Airy-N 2 𝑥 {\displaystyle{\displaystyle x^{2}{M^{2}}\left(x\right)={N'^{2}}\left(x\right)% +{N^{2}}\left(x\right){\phi'^{2}}\left(x\right)={N'^{2}}\left(x\right)+\pi^{-2% }x^{2}{N^{-2}}\left(x\right),}}
    0 references
    DLMF id
    DLMF:9.8.E16
    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
    Airy modulus function
    test
    M ⁡ ( z ) modulus-Airy-M 𝑧 {\displaystyle{\displaystyle M\left(\NVar{z}\right)}}
    xml-id
    C9.S8.E3.m2agdec
    0 references
    Airy modulus function
    test
    N ⁡ ( z ) modulus-Airy-N 𝑧 {\displaystyle{\displaystyle N\left(\NVar{z}\right)}}
    xml-id
    C9.S8.E7.m2agdec
    0 references
    Airy phase function
    test
    ϕ ⁡ ( z ) phase-Airy-Phi 𝑧 {\displaystyle{\displaystyle\phi\left(\NVar{z}\right)}}
    xml-id
    C9.S8.E8.m2afdec
    0 references
    Q11382
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C9.S1.XMD2.m1odec
    0 references
     
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