DLMF:28.28.E47

MaRDI QIDQ9170

• Label: DLMF:28.28.E47

Digital Library of Mathematical Functions ID 28.28.E47

${\displaystyle{\displaystyle\dfrac{\sinh z}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\cos t\mathrm{ce}_{n}\left(t,h^{2}\right)\mathrm{ce}_{m}\left(t,h^{2}\right)}{{\sinh^{2}}z+{\sin^{2}}t}\mathrm{d}t=(-1)^{p+1}\mathrm{i}h\widehat{\alpha}_{n,m}^{(c)}\mathrm{Dc}_{0}\left(n,m,z\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Dc}_{\NVar{j}}\left(\NVar{n},\NVar{m},\NVar{z}\right)}}$: cross-products of radial Mathieu functions and their derivatives
• ${\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle h}}$: parameter
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\widehat{\alpha}_{n,m}}}$: 28.28.E49
 

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