Formula:9093

Digital Library of Mathematical Functions ID 28.24.E3

${\displaystyle{\displaystyle{\mathrm{Mc}^{(j)}_{2m+1}}\left(z,h\right)=(-1)^{m}\sum_{\ell=0}^{\infty}(-1)^{\ell}\frac{A_{2\ell+1}^{2m+1}(h^{2})}{A_{2s+1}^{2m+1}(h^{2})}\left(J_{\ell-s}\left(he^{-z}\right){\cal C}_{\ell+s+1}^{(j)}(he^{z})+J_{\ell+s+1}\left(he^{-z}\right){\cal C}_{\ell-s}^{(j)}(he^{z})\right),}}$

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

Resources that cite this formula

No records found.