Formula:9098

Digital Library of Mathematical Functions ID 28.24.E8

${\displaystyle{\displaystyle\mathrm{Ie}_{2m+1}\left(z,h\right)=(-1)^{s}\sum_{\ell=0}^{\infty}(-1)^{\ell}\dfrac{B_{2\ell+1}^{2m+1}(h^{2})}{B_{2s+1}^{2m+1}(h^{2})}\left(I_{\ell-s}\left(he^{-z}\right)I_{\ell+s+1}\left(he^{z}\right)+I_{\ell+s+1}\left(he^{-z}\right)I_{\ell-s}\left(he^{z}\right)\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$: modified Bessel function of the first kind
• ${\displaystyle{\displaystyle\mathrm{Ie}_{\NVar{n}}\left(\NVar{z},\NVar{h}\right)}}$: modified Mathieu function
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle h}}$: parameter
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle B_{m}(q)}}$: Fourier coefficient
 

Resources that cite this formula

No records found.