Results 1 to 4 of 4

Math Help - Even power of cosine and double factorial

  1. #1
    Newbie DSYEAY's Avatar
    Joined
    Mar 2011
    From
    Singapore
    Posts
    4

    Wink Even power of cosine and double factorial

    The first elementary paper i'm publising here
    Hope to hear some comments
    Attached Thumbnails Attached Thumbnails Even power of cosine and double factorial-even-power-cosine-double-factorial.pdf  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,838
    Thanks
    320
    Awards
    1
    Quote Originally Posted by DSYEAY View Post
    The first elementary paper i'm publising here
    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
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by DSYEAY View Post
    The first elementary paper i'm publising here
    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\int_0^{k\pi}\!\!\!\cos^{2n}\theta\,d  \theta = \frac{(2k-1)!!}{(2k)!!}(k\pi) should read \displaystyle\int_0^{k\pi}\!\!\!\cos^{2n}\theta\,d  \theta = \frac{(2n-1)!!}{(2n)!!}(k\pi).

    Next, in the statement of Lemma 1, 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 \frac12\pi, not \frac12.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie DSYEAY's Avatar
    Joined
    Mar 2011
    From
    Singapore
    Posts
    4
    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...

    __________________________________________________ _________________________

    Editted Paper:

    Download Link
    Last edited by DSYEAY; March 17th 2011 at 11:28 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: June 22nd 2011, 12:43 PM
  2. Why is cosine(-x) equal to cosine(x)?
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: August 6th 2010, 05:56 PM
  3. Replies: 1
    Last Post: October 30th 2009, 10:27 AM
  4. cosine of a double angle
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 22nd 2009, 03:00 PM
  5. Power Series w/ factorial
    Posted in the Calculus Forum
    Replies: 7
    Last Post: April 8th 2009, 08:45 PM

Search Tags


/mathhelpforum @mathhelpforum