DLMF:10.68.E2 (Q3863)

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DLMF:10.68.E2
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    Statements

    Defining formula
    N ν ⁡ ( x ) ⁢ e i ⁢ ϕ ν ⁡ ( x ) = ker ν ⁡ x + i ⁢ kei ν ⁡ x , modulus-Bessel-N 𝜈 𝑥 superscript 𝑒 𝑖 phase-Bessel-Phi 𝜈 𝑥 Kelvin-ker 𝜈 𝑥 𝑖 Kelvin-kei 𝜈 𝑥 {\displaystyle{\displaystyle N_{\nu}\left(x\right)e^{i\phi_{\nu}\left(x\right)% }=\operatorname{ker}_{\nu}x+i\operatorname{kei}_{\nu}x,}}
    0 references
    DLMF id
    DLMF:10.68.E2
    0 references
    Symbols used
    Kelvin function
    Defining formula
    kei ν ⁡ ( x ) Kelvin-kei 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{kei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E2.m3adec
    0 references
    Kelvin function
    Defining formula
    ker ν ⁡ ( x ) Kelvin-ker 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{ker}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E2.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    modulus of derivatives of Bessel functions
    Defining formula
    N ν ⁡ ( x ) modulus-Bessel-N 𝜈 𝑥 {\displaystyle{\displaystyle N_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S18.E2.m2adec
    0 references
    Q11445
    Defining formula
    ϕ ν ⁡ ( x ) phase-Bessel-Phi 𝜈 𝑥 {\displaystyle{\displaystyle\phi_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S18.E3.m2adec
    0 references
    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1adec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1adec
    0 references
     
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