/sci/ - Science & Math

>>15280216
heres my attempt:
we can rewrite the denominator like
[eqn]
\int_0^x \frac{(a^4-1)t^2 + 1}{\sqrt{-t^2((a^4-1)t^2+1)+(a^4-1)t^2+1}} dt
[/eqn]
then do a substitution like this, hopefully its all correct
[eqn]
u = (a^4-1)t^2+1 \\
t = \sqrt{\frac{u-1}{a^4-1}} \\
du = 2(a^4-1)t \; dt \\
dt = \frac{du}{2(a^4-1)t} = \frac{du}{2\sqrt{(a^4-1)(u-1)}} \\
\arcsin(x) = \int_0^{\sqrt{\frac{x-1}{a^4-1}}} \frac{u \; dt}{\sqrt{-t^2u+u}} = \int_0^{\sqrt{\frac{x-1}{a^4-1}}} \frac{u \; du}{\sqrt{-u^3+(a^4+1)u^2-a^4u}}
[/eqn]
which is soooo close, but theres no constant term.

>>15058982
>If x[n] = u[n], then does x[n-1] = u[n-1]?
yea

>>11769011
>This uniqueness of analytic continuation is a rather amazing and extremely powerful statement. It says in effect that knowing the value of a complex function in some finite complex domain uniquely determines the value of the function at every other point.
thats kinda what i was think of. thanks anon

>>11641437
np