Formula:9080

Digital Library of Mathematical Functions ID 28.23.E3

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \Mathieume{\nu}'@{0}{h^{2}}\modMathieuM{j}{\nu}@{z}{h}=\iunit\tanh@@{z}\sum_{n=-\infty}^{\infty}(-1)^{n}(\nu+2n)c_{2n}^{\nu}(h^{2}){\cal C}_{\nu+2n}^{(j)}(2h\cosh@@{z}),}

Symbols List

• ${\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)}}$:
• ${\displaystyle{\displaystyle\cosh\NVar{z}}}$: hyperbolic cosine function
• ${\displaystyle{\displaystyle\tanh\NVar{z}}}$: hyperbolic tangent function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{z},\NVar{h}\right)}}$:
• ${\displaystyle{\displaystyle h}}$: parameter
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle j}}$: integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
• ${\displaystyle{\displaystyle c_{2m}(q)}}$: coefficients
• ${\displaystyle{\displaystyle\mathcal{C}_{\mu}^{(j)}}}$: cylinder functions
 

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