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DLMF:10.68.E8 - MaRDI portal

DLMF:10.68.E8 (Q4571)

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DLMF:10.68.E8
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    Statements

    DLMF defining formula
    ber ν ′ ⁡ x = 1 2 ⁢ M ν + 1 ⁢ cos ⁡ ( θ ν + 1 - 1 4 ⁢ π ) - 1 2 ⁢ M ν - 1 ⁢ cos ⁡ ( θ ν - 1 - 1 4 ⁢ π ) = ( ν / x ) ⁢ M ν ⁢ cos ⁡ θ ν + M ν + 1 ⁢ cos ⁡ ( θ ν + 1 - 1 4 ⁢ π ) = - ( ν / x ) ⁢ M ν ⁢ cos ⁡ θ ν - M ν - 1 ⁢ cos ⁡ ( θ ν - 1 - 1 4 ⁢ π ) , diffop Kelvin-ber 𝜈 1 𝑥 1 2 modulus-Bessel-M 𝜈 1 phase-Bessel-Theta 𝜈 1 1 4 𝜋 1 2 modulus-Bessel-M 𝜈 1 phase-Bessel-Theta 𝜈 1 1 4 𝜋 𝜈 𝑥 modulus-Bessel-M 𝜈 phase-Bessel-Theta 𝜈 modulus-Bessel-M 𝜈 1 phase-Bessel-Theta 𝜈 1 1 4 𝜋 𝜈 𝑥 modulus-Bessel-M 𝜈 phase-Bessel-Theta 𝜈 modulus-Bessel-M 𝜈 1 phase-Bessel-Theta 𝜈 1 1 4 𝜋 {\displaystyle{\displaystyle\operatorname{ber}_{\nu}'x=\tfrac{1}{2}M_{\nu+1}% \cos\left(\theta_{\nu+1}-\tfrac{1}{4}\pi\right)-\tfrac{1}{2}M_{\nu-1}\cos\left% (\theta_{\nu-1}-\tfrac{1}{4}\pi\right)=(\nu/x)M_{\nu}\cos\theta_{\nu}+M_{\nu+1% }\cos\left(\theta_{\nu+1}-\tfrac{1}{4}\pi\right)=-(\nu/x)M_{\nu}\cos\theta_{% \nu}-M_{\nu-1}\cos\left(\theta_{\nu-1}-\tfrac{1}{4}\pi\right),}}
    0 references
    Symbols used
    Kelvin function
    DLMF defining formula
    ber ν ⁡ ( x ) Kelvin-ber 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E1.m2addec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    cosine function
    DLMF defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
    0 references
    modulus of Bessel functions
    DLMF defining formula
    M ν ⁡ ( x ) modulus-Bessel-M 𝜈 𝑥 {\displaystyle{\displaystyle M_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S18.E1.m2addec
    0 references
    phase of Bessel functions
    DLMF defining formula
    θ ν ⁡ ( x ) phase-Bessel-Theta 𝜈 𝑥 {\displaystyle{\displaystyle\theta_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S18.E3.m1addec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1gdec
    0 references
    complex parameter
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1fdec
    0 references

    Identifiers

     
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