Formula:6906

Digital Library of Mathematical Functions ID 19.8.E4

${\displaystyle{\displaystyle\frac{1}{M\left(a_{0},g_{0}\right)}=\frac{2}{\pi}\int_{0}^{\pi/2}\frac{\mathrm{d}\theta}{\sqrt{a_{0}^{2}{\cos^{2}}\theta+g_{0}^{2}{\sin^{2}}\theta}}=\frac{1}{\pi}\int_{0}^{\infty}\frac{\mathrm{d}t}{\sqrt{t(t+a_{0}^{2})(t+g_{0}^{2})}}.}}$

Symbols List

• ${\displaystyle{\displaystyle M\left(\NVar{a},\NVar{g}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: 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
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle a_{n}}}$: iterate
• ${\displaystyle{\displaystyle g_{n}}}$: iterate
 

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