DLMF:28.23.E2 (Q8386)

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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
     
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