Formula:9082

Digital Library of Mathematical Functions ID 28.23.E5

${\displaystyle{\displaystyle\mathrm{me}_{\nu}'\left(\tfrac{1}{2}\pi,h^{2}\right){\mathrm{M}^{(j)}_{\nu}}\left(z,h\right)=\mathrm{i}e^{\mathrm{i}\nu\ifrac{\pi}{2}}\coth z\sum_{n=-\infty}^{\infty}(\nu+2n)c_{2n}^{\nu}(h^{2}){\cal C}_{\nu+2n}^{(j)}(2h\sinh z),}}$

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
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\coth\NVar{z}}}$: hyperbolic cotangent function
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine 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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