DLMF:9.8.E16 (Q2850)

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DLMF:9.8.E16
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    Statements

    Defining formula
    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
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    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.m2agdec
    0 references
     
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