DLMF:28.24.E13 (Q8410): Difference between revisions

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DLMF:28.24.E13
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    Defining formula
    Ko 2 ⁢ m + 1 ⁡ ( z , h ) = ∑ ℓ = 0 ∞ A 2 ⁢ ℓ + 1 2 ⁢ m + 1 ⁢ ( h 2 ) A 2 ⁢ s + 1 2 ⁢ m + 1 ⁢ ( h 2 ) ⁢ ( I ℓ - s ⁡ ( h ⁢ e - z ) ⁢ K ℓ + s + 1 ⁡ ( h ⁢ e z ) + I ℓ + s + 1 ⁡ ( h ⁢ e - z ) ⁢ K ℓ - s ⁡ ( h ⁢ e z ) ) . modified-Mathieu-Ko 2 𝑚 1 𝑧 ℎ superscript subscript ℓ 0 superscript subscript 𝐴 2 ℓ 1 2 𝑚 1 superscript ℎ 2 superscript subscript 𝐴 2 𝑠 1 2 𝑚 1 superscript ℎ 2 modified-Bessel-first-kind ℓ 𝑠 ℎ superscript 𝑒 𝑧 modified-Bessel-second-kind ℓ 𝑠 1 ℎ superscript 𝑒 𝑧 modified-Bessel-first-kind ℓ 𝑠 1 ℎ superscript 𝑒 𝑧 modified-Bessel-second-kind ℓ 𝑠 ℎ superscript 𝑒 𝑧 {\displaystyle{\displaystyle\mathrm{Ko}_{2m+1}\left(z,h\right)=\sum_{\ell=0}^{% \infty}\frac{A_{2\ell+1}^{2m+1}(h^{2})}{A_{2s+1}^{2m+1}(h^{2})}\left(I_{\ell-s% }\left(he^{-z}\right)K_{\ell+s+1}\left(he^{z}\right)+I_{\ell+s+1}\left(he^{-z}% \right)K_{\ell-s}\left(he^{z}\right)\right).}}
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    DLMF id
    DLMF:28.24.E13
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