Results 1 to 3 of 3

Math Help - gamma function algebra...

  1. #1
    Newbie
    Joined
    Sep 2007
    Posts
    2

    gamma function algebra...

    Wasn't sure which forum to put this in, I've done the probability part - it's just that my answer is a few lines away from the sample solution I've been given, and I don't understand what they've done.

    My answer is

    (2^k/sqrt(pi))(k - 1/2)(k - 3/2) ... ... (3/2)(1/2)Gamma(1/2)

    The next line of working for the sample solution is

    (2k - 1)(2k - 3) ... ... (3)

    I see that the sqrt(pi) and the gamma(1/2) cancel, other than that I'm stuck!

    Any help would be much appreciated. not sure if it's needed or not, but k = n/2 where n is an positive even integer
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,054
    Thanks
    368
    Awards
    1
    Quote Originally Posted by PiePie View Post
    Wasn't sure which forum to put this in, I've done the probability part - it's just that my answer is a few lines away from the sample solution I've been given, and I don't understand what they've done.

    My answer is

    (2^k/sqrt(pi))(k - 1/2)(k - 3/2) ... ... (3/2)(1/2)Gamma(1/2)

    The next line of working for the sample solution is

    (2k - 1)(2k - 3) ... ... (3)

    I see that the sqrt(pi) and the gamma(1/2) cancel, other than that I'm stuck!

    Any help would be much appreciated. not sure if it's needed or not, but k = n/2 where n is an positive even integer
    Unless you have a specific value for k the best you can do is
    (2k - 1)(2k - 3)~ ... ~3 \cdot 1 = (2k - 1)!!
    where (2k - 1)!! is the "odd factorial function." It multiplies only the odd numbers up to (2k - 1).

    (In case you were wondering there is an even factorial function that is a product of only even numbers, and it has the same symbol, "!!" The nice thing about this is you don't really need to use it:
    (2n)!! = 2^n \cdot n!)

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2007
    Posts
    2
    Thanks for the reply... I actually meant I don't understand how to go from the first line I posted to the second. Sorry for the confusion...
    I think I just don't understand what happens to the "k" index?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Gamma Function
    Posted in the Differential Geometry Forum
    Replies: 7
    Last Post: March 24th 2011, 09:40 PM
  2. [SOLVED] The error function and incomplete gamma function
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: January 31st 2010, 03:24 PM
  3. gamma function
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: December 1st 2009, 12:29 PM
  4. The Gamma Function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 9th 2009, 10:58 PM
  5. the min. value of gamma function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 10th 2009, 09:27 AM

Search Tags


/mathhelpforum @mathhelpforum