Formula:9152

Digital Library of Mathematical Functions ID 28.28.E33

${\displaystyle{\displaystyle\gamma_{\nu,m}=\dfrac{1}{2\pi}\int_{0}^{2\pi}\mathrm{me}_{\nu}'\left(t\right)\mathrm{me}_{-\nu-2m}\left(t\right)\mathrm{d}t=(-1)^{m}\dfrac{4\mathrm{i}}{\pi}\frac{\mathrm{me}_{\nu}'\left(0\right)\mathrm{me}_{-\nu-2m}\left(0\right)}{\mathrm{D}_{1}\left(\nu,\nu+2m,0\right)}.}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{D}_{\NVar{j}}\left(\NVar{\nu},\NVar{\mu},\NVar{z}\right)}}$: cross-products of modified Mathieu functions and their derivatives
• ${\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle h}}$: parameter
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

Resources that cite this formula

No records found.