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DLMF:10.18.E12 - MaRDI portal

DLMF:10.18.E12 (Q3903)

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DLMF:10.18.E12
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    Statements

    DLMF defining formula
    M ν ⁡ ( x ) ⁢ N ν ⁡ ( x ) ⁢ sin ⁡ ( ϕ ν ⁡ ( x ) - θ ν ⁡ ( x ) ) = 2 π ⁢ x . modulus-Bessel-M 𝜈 𝑥 modulus-Bessel-N 𝜈 𝑥 phase-Bessel-Phi 𝜈 𝑥 phase-Bessel-Theta 𝜈 𝑥 2 𝜋 𝑥 {\displaystyle{\displaystyle M_{\nu}\left(x\right)N_{\nu}\left(x\right)\sin% \left(\phi_{\nu}\left(x\right)-\theta_{\nu}\left(x\right)\right)=\frac{2}{\pi x% }.}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    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.m2agdec
    0 references
    modulus of derivatives of Bessel functions
    DLMF defining formula
    N ν ⁡ ( x ) modulus-Bessel-N 𝜈 𝑥 {\displaystyle{\displaystyle N_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S18.E2.m2afdec
    0 references
    phase of derivatives of Bessel functions
    DLMF defining formula
    ϕ ν ⁡ ( x ) phase-Bessel-Phi 𝜈 𝑥 {\displaystyle{\displaystyle\phi_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S18.E3.m2afdec
    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.m1agdec
    0 references
    sine function
    DLMF defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2abdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1kdec
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    complex parameter
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1kdec
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    Identifiers

     
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