DLMF:28.23.E2 (Q8386): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12272 / rank
 
Normal rank
Property / Symbols used: Q12272 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12272 / qualifier
 
xml-id: C28.S1.XMD6.m1dec

Revision as of 15:06, 2 January 2020

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DLMF:28.23.E2
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    Statements

    Defining formula
    me ν ⁡ ( 0 , h 2 ) ⁢ M ν ( j ) ⁡ ( z , h ) = ∑ n = - ∞ ∞ ( - 1 ) n ⁢ c 2 ⁢ n ν ⁢ ( h 2 ) ⁢ 𝒞 ν + 2 ⁢ n ( j ) ⁢ ( 2 ⁢ h ⁢ cosh ⁡ z ) , Mathieu-me 𝜈 0 superscript ℎ 2 modified-Mathieu-M 𝑗 𝜈 𝑧 ℎ superscript subscript 𝑛 superscript 1 𝑛 superscript subscript 𝑐 2 𝑛 𝜈 superscript ℎ 2 superscript subscript 𝒞 𝜈 2 𝑛 𝑗 2 ℎ 𝑧 {\displaystyle{\displaystyle\mathrm{me}_{\nu}\left(0,h^{2}\right){\mathrm{M}^{% (j)}_{\nu}}\left(z,h\right)=\sum_{n=-\infty}^{\infty}(-1)^{n}c_{2n}^{\nu}(h^{2% }){\cal C}_{\nu+2n}^{(j)}(2h\cosh z),}}
    0 references
    DLMF id
    DLMF:28.23.E2
    0 references
    Symbols used
    Q12299
    Defining formula
    me n ⁡ ( z , q ) Mathieu-me 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S12.SS2.p2.m2adec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.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.m4adec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1dec
    0 references
    Q12279
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C28.S1.XMD2.m1dec
    0 references
    Q12291
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C28.S1.XMD3.m1adec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1dec
    0 references
     
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