DLMF:28.20.E11 (Q8343): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12278 / rank
 
Normal rank
Property / Symbols used: Q12278 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q12278 / qualifier
 
xml-id: C28.S1.XMD7.m1edec

Latest revision as of 15:01, 2 January 2020

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DLMF:28.20.E11
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    Statements

    Defining formula
    M ν ( 1 ) ⁡ ( z , h ) = J ν ⁡ ( 2 ⁢ h ⁢ cosh ⁡ z ) + e | ℑ ⁡ ( 2 ⁢ h ⁢ cosh ⁡ z ) | ⁢ O ⁡ ( ( sech ⁡ z ) 3 / 2 ) , modified-Mathieu-M 1 𝜈 𝑧 ℎ Bessel-J 𝜈 2 ℎ 𝑧 superscript 𝑒 2 ℎ 𝑧 Big-O superscript 𝑧 3 2 {\displaystyle{\displaystyle{\mathrm{M}^{(1)}_{\nu}}\left(z,h\right)=J_{\nu}% \left(2h\cosh z\right)+e^{|\Im(2h\cosh z)|}O\left(\left(\operatorname{sech}z% \right)^{3/2}\right),}}
    0 references
    DLMF id
    DLMF:28.20.E11
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2adec
    0 references
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2abdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2addec
    0 references
    hyperbolic secant function
    Defining formula
    sech ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}
    xml-id
    C4.S28.E6.m2abdec
    0 references
    Q10901
    Defining formula
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2adec
    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.m4abdec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1cdec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1idec
    0 references
    Q12278
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C28.S1.XMD7.m1edec
    0 references
     
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