DLMF:9.8.E17 (Q2851)

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DLMF:9.8.E17
No description defined

    Statements

    Defining formula
    tan ⁡ ( θ ⁡ ( x ) - ϕ ⁡ ( x ) ) = 1 / ( π ⁢ M ⁡ ( x ) ⁢ M ′ ⁡ ( x ) ) = - M ⁡ ( x ) ⁢ θ ′ ⁡ ( x ) / M ′ ⁡ ( x ) , phase-Airy-Theta 𝑥 phase-Airy-Phi 𝑥 1 𝜋 modulus-Airy-M 𝑥 diffop modulus-Airy-M 1 𝑥 modulus-Airy-M 𝑥 diffop phase-Airy-Theta 1 𝑥 diffop modulus-Airy-M 1 𝑥 {\displaystyle{\displaystyle\tan\left(\theta\left(x\right)-\phi\left(x\right)% \right)=1/(\pi M\left(x\right)M'\left(x\right))=-M\left(x\right)\theta'\left(x% \right)/M'\left(x\right),}}
    0 references
    DLMF id
    DLMF:9.8.E17
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    Airy modulus function
    Defining formula
    M ⁡ ( z ) modulus-Airy-M 𝑧 {\displaystyle{\displaystyle M\left(\NVar{z}\right)}}
    xml-id
    C9.S8.E3.m2ahdec
    0 references
    Airy phase function
    Defining formula
    ϕ ⁡ ( z ) phase-Airy-Phi 𝑧 {\displaystyle{\displaystyle\phi\left(\NVar{z}\right)}}
    xml-id
    C9.S8.E8.m2agdec
    0 references
    Airy phase function
    Defining formula
    θ ⁡ ( z ) phase-Airy-Theta 𝑧 {\displaystyle{\displaystyle\theta\left(\NVar{z}\right)}}
    xml-id
    C9.S8.E4.m2agdec
    0 references
    tangent function
    Defining formula
    tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    xml-id
    C4.S14.E4.m2adec
    0 references
    Q11382
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C9.S1.XMD2.m1pdec
    0 references
     
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