Formula:9168

Digital Library of Mathematical Functions ID 28.28.E45

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \dfrac{\sinh@{2z}}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\Mathieuse{n}'@{t}{h^{2}}\Mathieuce{m}@{t}{h^{2}}}{\sinh^{2}@@{z}+\sin^{2}@@{t}}\diff{t}=(-1)^{p+1}\iunit\widehat{\gamma}_{n,m}\radMathieuDsc{1}@{n}{m}{z},}

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Dsc}_{\NVar{j}}\left(\NVar{n},\NVar{m},\NVar{z}\right)}}$: cross-products of radial Mathieu functions and their derivatives
• ${\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)}}$:
• ${\displaystyle{\displaystyle\mathrm{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: 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
• ${\displaystyle{\displaystyle\widehat{\gamma}_{n,m}}}$: 28.28.E46
 

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