find-F-a-0-1-1-a-2-t-2-1-t-2-dt-for-background-see-Q127811-

Question Number 127925 by mr W last updated on 03/Jan/21

f i n d F (a) = \int_{0}^{1} \sqrt{\frac{1 + a^{2} t^{2}}{1 - t^{2}}} d t

f o r b a c k g r o u n d s e e Q 127811 .

Answered by mindispower last updated on 03/Jan/21

= \int_{0}^{1} \sqrt{\frac{1 - (- {(a)}^{2}) t^{2}}{1 - t^{2}}} d t = E (1 ∣ - a^{2})

E e l e p t i c i n t e g r a l o f 2 n d k i n d

E (x ∣ k^{2}) = \int_{0}^{x} \frac{\sqrt{1 - k^{2} t^{2}}}{\sqrt{1 - t^{2}}} d t

Commented by mr W last updated on 03/Jan/21

t h a n k s s i r!

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