DLMF:28.20.E10 (Q8342)

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DLMF:28.20.E10
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    Statements

    Defining formula
    M ν ( 4 ) ⁡ ( z , h ) = H ν ( 2 ) ⁡ ( 2 ⁢ h ⁢ cosh ⁡ z ) ⁢ ( 1 + O ⁡ ( sech ⁡ z ) ) , modified-Mathieu-M 4 𝜈 𝑧 ℎ Hankel-H-2-Bessel-third-kind 𝜈 2 ℎ 𝑧 1 Big-O 𝑧 {\displaystyle{\displaystyle{\mathrm{M}^{(4)}_{\nu}}\left(z,h\right)={H^{(2)}_% {\nu}}\left(2h\cosh z\right)\left(1+O\left(\operatorname{sech}z\right)\right),}}
    0 references
    DLMF id
    DLMF:28.20.E10
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aadec
    0 references
    Bessel function of the third kind (or Hankel function)
    Defining formula
    H ν ( 2 ) ⁡ ( z ) Hankel-H-2-Bessel-third-kind 𝜈 𝑧 {\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E6.m2adec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2acdec
    0 references
    hyperbolic secant function
    Defining formula
    sech ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}
    xml-id
    C4.S28.E6.m2aadec
    0 references
    Q12301
    Defining formula
    M ν ( j ) ⁡ ( z , h ) modified-Mathieu-M 𝑗 𝜈 𝑧 ℎ {\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{% z},\NVar{h}\right)}}
    xml-id
    C28.S20.SS3.p1.m4aadec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1bdec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1hdec
    0 references
    Q12278
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C28.S1.XMD7.m1ddec
    0 references
     
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