DLMF:28.23.E8 (Q8392)

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DLMF:28.23.E8
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    Statements

    Defining formula
    Mc 2 ⁢ m + 1 ( j ) ⁡ ( z , h ) = ( - 1 ) m ⁢ ( ce 2 ⁢ m + 1 ⁡ ( 0 , h 2 ) ) - 1 ⁢ ∑ ℓ = 0 ∞ ( - 1 ) ℓ ⁢ A 2 ⁢ ℓ + 1 2 ⁢ m + 1 ⁢ ( h 2 ) ⁢ 𝒞 2 ⁢ ℓ + 1 ( j ) ⁢ ( 2 ⁢ h ⁢ cosh ⁡ z ) , modified-Mathieu-Mc 𝑗 2 𝑚 1 𝑧 ℎ superscript 1 𝑚 superscript Mathieu-ce 2 𝑚 1 0 superscript ℎ 2 1 superscript subscript ℓ 0 superscript 1 ℓ superscript subscript 𝐴 2 ℓ 1 2 𝑚 1 superscript ℎ 2 superscript subscript 𝒞 2 ℓ 1 𝑗 2 ℎ 𝑧 {\displaystyle{\displaystyle{\mathrm{Mc}^{(j)}_{2m+1}}\left(z,h\right)=(-1)^{m% }\left(\mathrm{ce}_{2m+1}\left(0,h^{2}\right)\right)^{-1}\sum_{\ell=0}^{\infty% }(-1)^{\ell}A_{2\ell+1}^{2m+1}(h^{2}){\cal C}_{2\ell+1}^{(j)}(2h\cosh z),}}
    0 references
    DLMF id
    DLMF:28.23.E8
    0 references
    Symbols used
    Q12283
    Defining formula
    ce n ⁡ ( z , q ) Mathieu-ce 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S2.SS6.p1.m7abdec
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