DLMF:28.20.E10 (Q8342): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: hyperbolic cosine function / rank
 
Normal rank
Property / Symbols used: hyperbolic cosine function / qualifier
 
Defining formula:

cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}

\cosh@@{\NVar{z}}
Property / Symbols used: hyperbolic cosine function / qualifier
 
xml-id: C4.S28.E2.m2acdec

Revision as of 15:01, 2 January 2020

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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
     
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