Formula:9092

Digital Library of Mathematical Functions ID 28.24.E2

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \varepsilon_{s}\radMathieuMc{j}{2m}@{z}{h}=(-1)^{m}\sum_{\ell=0}^{\infty}(-1)^{\ell}\frac{A_{2\ell}^{2m}(h^{2})}{A_{2s}^{2m}(h^{2})}\left(\BesselJ{\ell-s}@{he^{-z}}{\cal C}_{\ell+s}^{(j)}(he^{z})+\BesselJ{\ell+s}@{he^{-z}}{\cal C}_{\ell-s}^{(j)}(he^{z})\right),}

Symbols List

• ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$: Bessel function of the first kind
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle{\mathrm{Mc}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z},\NVar{h}\right)}}$: radial Mathieu function
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle h}}$: parameter
• ${\displaystyle{\displaystyle j}}$: integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\mathcal{C}_{\mu}^{(j)}}}$: cylinder functions
• ${\displaystyle{\displaystyle\varepsilon_{s}}}$: constants
• ${\displaystyle{\displaystyle A_{m}(q)}}$: Fourier coefficient
 

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