Formula:9086

Digital Library of Mathematical Functions ID 28.23.E9

${\displaystyle{\displaystyle{\mathrm{Mc}^{(j)}_{2m+1}}\left(z,h\right)=(-1)^{m+1}\left(\mathrm{ce}_{2m+1}'\left(\tfrac{1}{2}\pi,h^{2}\right)\right)^{-1}\coth z\sum_{\ell=0}^{\infty}(2\ell+1)A_{2\ell+1}^{2m+1}(h^{2}){\cal C}_{2\ell+1}^{(j)}(2h\sinh z),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\coth\NVar{z}}}$: hyperbolic cotangent function
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle{\mathrm{Mc}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z},\NVar{h}\right)}}$: 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
• ${\displaystyle{\displaystyle A_{m}(q)}}$: Fourier coefficient
 

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