DLMF:10.68.E1 (Q3862)

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DLMF:10.68.E1
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    Statements

    Defining formula
    M ν ⁡ ( x ) ⁢ e i ⁢ θ ν ⁡ ( x ) = ber ν ⁡ x + i ⁢ bei ν ⁡ x , modulus-Bessel-M 𝜈 𝑥 superscript 𝑒 𝑖 phase-Bessel-Theta 𝜈 𝑥 Kelvin-ber 𝜈 𝑥 𝑖 Kelvin-bei 𝜈 𝑥 {\displaystyle{\displaystyle M_{\nu}\left(x\right)e^{i\theta_{\nu}\left(x% \right)}=\operatorname{ber}_{\nu}x+i\operatorname{bei}_{\nu}x,}}
    0 references
    DLMF id
    DLMF:10.68.E1
    0 references
    Symbols used
    Kelvin function
    Defining formula
    bei ν ⁡ ( x ) Kelvin-bei 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E1.m3adec
    0 references
    Kelvin function
    Defining formula
    ber ν ⁡ ( x ) Kelvin-ber 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E1.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    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.m2adec
    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.m1adec
    0 references
    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1dec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1dec
    0 references
     
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