I hate Frobenius series, can anyone help

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Please find attached the problem I am having difficulty with its part (b) i need help with.

Cheers,

Dave:cry:
 

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What have you tried so far? I assume that you wrote out the equation in terms of the sum. What is that equation with r= 0?
 
HallsofIvy said:
What have you tried so far? I assume that you wrote out the equation in terms of the sum. What is that equation with r= 0?

Ya its just that it it gets really messy and I am not sure how to manipluate it properly do you, the eqn is what your supposed to get if you solve it with r =0 know any good sources on the internet for solving these things.

Cheers dave
 
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Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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