Formula:9221

Digital Library of Mathematical Functions ID 28.31.E12

${\displaystyle{\displaystyle\dfrac{1}{\pi}\int_{0}^{2\pi}\left(C_{p}^{m}(x,\xi)\right)^{2}\mathrm{d}x=\dfrac{1}{\pi}\int_{0}^{2\pi}\left(S_{p}^{m}(x,\xi)\right)^{2}\mathrm{d}x=1,}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\xi}}$: variable
• ${\displaystyle{\displaystyle C_{p}^{m}(z,\xi)}}$: Ince polynomials (locally)
• ${\displaystyle{\displaystyle S_{\NVar{p}}^{\NVar{m}}(\NVar{z},\\ NVar{xi})}}$: Ince polynomials (locally)
 

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