DLMF:28.23.E12 (Q8396)

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DLMF:28.23.E12
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    Statements

    Defining formula
    Ms 2 ⁢ m + 2 ( j ) ⁡ ( z , h ) = ( - 1 ) m ⁢ ( se 2 ⁢ m + 2 ′ ⁡ ( 0 , h 2 ) ) - 1 ⁢ tanh ⁡ z ⁢ ∑ ℓ = 0 ∞ ( - 1 ) ℓ ⁢ ( 2 ⁢ ℓ + 2 ) ⁢ B 2 ⁢ ℓ + 2 2 ⁢ m + 2 ⁢ ( h 2 ) ⁢ 𝒞 2 ⁢ ℓ + 2 ( j ) ⁢ ( 2 ⁢ h ⁢ cosh ⁡ z ) , modified-Mathieu-Ms 𝑗 2 𝑚 2 𝑧 ℎ superscript 1 𝑚 superscript diffop Mathieu-se 2 𝑚 2 1 0 superscript ℎ 2 1 𝑧 superscript subscript ℓ 0 superscript 1 ℓ 2 ℓ 2 superscript subscript 𝐵 2 ℓ 2 2 𝑚 2 superscript ℎ 2 superscript subscript 𝒞 2 ℓ 2 𝑗 2 ℎ 𝑧 {\displaystyle{\displaystyle{\mathrm{Ms}^{(j)}_{2m+2}}\left(z,h\right)=(-1)^{m% }\left(\mathrm{se}_{2m+2}'\left(0,h^{2}\right)\right)^{-1}\tanh z\sum_{\ell=0}% ^{\infty}(-1)^{\ell}(2\ell+2)B_{2\ell+2}^{2m+2}(h^{2}){\cal C}_{2\ell+2}^{(j)}% (2h\cosh z),}}
    0 references
    DLMF id
    DLMF:28.23.E12
    0 references
    Symbols used
    Q12286
    Defining formula
    se n ⁡ ( z , q ) Mathieu-se 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}
    xml-id
    C28.S2.SS6.p1.m8abdec
    0 references
     
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