Formula:9091

Digital Library of Mathematical Functions ID 28.24.E1

${\displaystyle{\displaystyle c_{2n}^{\nu}(h^{2}){\mathrm{M}^{(j)}_{\nu}}\left(z,h\right)=\sum_{\ell=-\infty}^{\infty}(-1)^{\ell}c_{2\ell}^{\nu}(h^{2})J_{\ell-n}\left(he^{-z}\right)\mathcal{C}_{\nu+n+\ell}^{(j)}(he^{z}),}}$

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
• ${\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{z},\NVar{h}\right)}}$:
• ${\displaystyle{\displaystyle h}}$: 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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