Formula:9133

Digital Library of Mathematical Functions ID 28.28.E17

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \dfrac{1}{\pi}\int_{0}^{\pi}\mathcal{C}^{(j)}_{\nu+2s}(2hR)e^{-\iunit(\nu+2s)\phi}\Mathieume{\nu}@{t}{h^{2}}\diff{t}=(-1)^{s}c^{\nu}_{2s}(h^{2})\modMathieuM{j}{\nu}@{z}{h},}

Constraint(s)

${\displaystyle{\displaystyle s\in\mathbb{Z}}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\mathbb{Z}}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{z},\NVar{h}\right)}}$:
• ${\displaystyle{\displaystyle h}}$: parameter
• ${\displaystyle{\displaystyle j}}$: 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
• ${\displaystyle{\displaystyle\phi(z,t)}}$: function
• ${\displaystyle{\displaystyle R(z,t)}}$: function
 

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