DLMF:10.68.E11 (Q3878)

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DLMF:10.68.E11
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    Statements

    Defining formula
    M ν ′ = ( ν / x ) ⁢ M ν + M ν + 1 ⁢ cos ⁡ ( θ ν + 1 - θ ν - 1 4 ⁢ π ) = - ( ν / x ) ⁢ M ν - M ν - 1 ⁢ cos ⁡ ( θ ν - 1 - θ ν - 1 4 ⁢ π ) , diffop modulus-Bessel-M 𝜈 1 𝜈 𝑥 modulus-Bessel-M 𝜈 modulus-Bessel-M 𝜈 1 phase-Bessel-Theta 𝜈 1 phase-Bessel-Theta 𝜈 1 4 𝜋 𝜈 𝑥 modulus-Bessel-M 𝜈 modulus-Bessel-M 𝜈 1 phase-Bessel-Theta 𝜈 1 phase-Bessel-Theta 𝜈 1 4 𝜋 {\displaystyle{\displaystyle M_{\nu}'=(\nu/x)M_{\nu}+M_{\nu+1}\cos\left(\theta% _{\nu+1}-\theta_{\nu}-\tfrac{1}{4}\pi\right)=-(\nu/x)M_{\nu}-M_{\nu-1}\cos% \left(\theta_{\nu-1}-\theta_{\nu}-\tfrac{1}{4}\pi\right),}}
    0 references
    DLMF id
    DLMF:10.68.E11
    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
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2addec
    0 references
    modulus of Bessel functions
    Defining formula
    M ν ⁡ ( x ) modulus-Bessel-M 𝜈 𝑥 {\displaystyle{\displaystyle M_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S18.E1.m2agdec
    0 references
    Q11444
    Defining formula
    θ ν ⁡ ( x ) phase-Bessel-Theta 𝜈 𝑥 {\displaystyle{\displaystyle\theta_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S18.E3.m1agdec
    0 references
    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1jdec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1hdec
    0 references
     
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