Formula:3624

Digital Library of Mathematical Functions ID 9.11.E19

${\displaystyle{\displaystyle\int_{0}^{\infty}\frac{\mathrm{d}t}{{\mathrm{Ai}^{2}}\left(t\right)+{\mathrm{Bi}^{2}}\left(t\right)}=\int_{0}^{\infty}\frac{t\mathrm{d}t}{{\mathrm{Ai}'^{2}}\left(t\right)+{\mathrm{Bi}'^{2}}\left(t\right)}=\frac{\pi^{2}}{6}.}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle M\left(\NVar{z}\right)}}$: Airy modulus function
• ${\displaystyle{\displaystyle N\left(\NVar{z}\right)}}$: Airy modulus function
• ${\displaystyle{\displaystyle\phi\left(\NVar{z}\right)}}$: Airy phase function
• ${\displaystyle{\displaystyle\theta\left(\NVar{z}\right)}}$: Airy phase function
• ${\displaystyle{\displaystyle x}}$: real variable
 

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