The first elementary paper i'm publising here (Hi)

Hope to hear some comments :)

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- Mar 17th 2011, 10:32 AMDSYEAYEven 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 AMtopsquark
- Mar 17th 2011, 11:50 AMOpalg
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 PMDSYEAY
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.

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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)

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