Can't understand the meaning of some symbols

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Homework Statement


This is an extract from elements of mechanics by giovanni.
I'[m unable to understand the meaning of R^d and C^\infty

http://flic.kr/p/9K8P7p

Homework Equations


The Attempt at a Solution

 
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hi shakgoku! :smile:

Rd is the same as Rn …

i assume "d" stands for "dimension" :biggrin:​

and C∞ is the space of functions which are differentiable "infinitely many" times
 
Hey tiny-tim!

Thank you , now everything in the page makes sense to me! :)
 

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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