DLMF:9.8.E15 (Q2849)

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DLMF:9.8.E15
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    Statements

    Defining formula
    N 2 ⁡ ( x ) = M ′ 2 ⁡ ( x ) + M 2 ⁡ ( x ) ⁢ θ ′ 2 ⁡ ( x ) = M ′ 2 ⁢ ( x ) + π - 2 ⁢ M - 2 ⁡ ( x ) , modulus-Airy-N 2 𝑥 diffop modulus-Airy-M 1 2 𝑥 modulus-Airy-M 2 𝑥 diffop phase-Airy-Theta 1 2 𝑥 diffop modulus-Airy-M 1 2 𝑥 superscript 𝜋 2 modulus-Airy-M 2 𝑥 {\displaystyle{\displaystyle{N^{2}}\left(x\right)={M'^{2}}\left(x\right)+{M^{2% }}\left(x\right){\theta'^{2}}\left(x\right)={M'^{2}}(x)+\pi^{-2}{M^{-2}}\left(% x\right),}}
    0 references
    DLMF id
    DLMF:9.8.E15
    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.m2addec
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    Airy modulus function
    Defining formula
    M ⁡ ( z ) modulus-Airy-M 𝑧 {\displaystyle{\displaystyle M\left(\NVar{z}\right)}}
    xml-id
    C9.S8.E3.m2afdec
    0 references
     
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