# Even power of cosine and double factorial

• Mar 17th 2011, 10:32 AM
DSYEAY
Even power of cosine and double factorial
The first elementary paper i'm publising here (Hi)
Hope to hear some comments :)
• Mar 17th 2011, 11:36 AM
topsquark
Quote:

Originally Posted by DSYEAY
The first elementary paper i'm publising here (Hi)
Hope to hear some comments :)

Nice little integral. I looked over your methods and they were good. But I found it simpler to integrate by parts and that method was not mentioned at all.

-Dan
• Mar 17th 2011, 11:50 AM
Opalg
Quote:

Originally Posted by DSYEAY
The first elementary paper i'm publising here (Hi)
Hope to hear some comments :)

The paper is essentially correct, but there are some careless misprints. For a start, in the result at the start of the paper, the indices k and n are confused. The result $\displaystyle \displaystyle\int_0^{k\pi}\!\!\!\cos^{2n}\theta\,d \theta = \frac{(2k-1)!!}{(2k)!!}(k\pi)$ should read $\displaystyle \displaystyle\int_0^{k\pi}\!\!\!\cos^{2n}\theta\,d \theta = \frac{(2n-1)!!}{(2n)!!}(k\pi)$.

Next, in the statement of Lemma 1, $\displaystyle A_k$ has not yet been defined. You should always define your notation before starting to use it.

Finally, in the section Proving the theorem by Mathematical Induction (First case of Finite Induction), the integral should be equal to $\displaystyle \frac12\pi$, not $\displaystyle \frac12.$
• Mar 17th 2011, 09:26 PM
DSYEAY
Hi Opalg! :)

Thank you for your time!
I will correct those mistake that i've made. I will also try to define those terms that i've used. Probably include a short abstract and talk also about second finite induction.

_______________________________________

Hi Dan :)

Thank you for your time!
I will include the part on integration by parts but essentially it will be very much alike to my Lemma 2. Will try to add more explanatory notes :)
Probably will add on the case for sine too or leave it for pratice for reader...

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Editted Paper: (Rofl)(Rofl)(Rofl)