MathGroup Archive 2002

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Trying to solve a sum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg36080] Re: Trying to solve a sum
  • From: "Borut L" <gollum at email.si>
  • Date: Wed, 21 Aug 2002 05:51:44 -0400 (EDT)
  • References: <ajfini$ipa$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

I don't think there is any simpler analytical solution.

Though, if you let n be large, the sum can be well aproximated by the gauss
integral, i.e. the error function.


bye,

Borut


"Constantine" <celster at cs.technion.ac.il> wrote in message
news:ajfini$ipa$1 at smc.vnet.net...
> Hi,
> I'm trying to solve the following sum:
>
> Sum[ p^(n-k) (1-p)^k Binomial[n, k] * (1+ n -2 k) / (1+n-k), {k, 0,
> Ceiling[n/2]} ]
>
> Pls, if anyone knows if that sum has a simple solution, I'll be pleasant
> for a hint how to find it.
>
> Thanks in advance.
> Constantine.
>
>
>
> P.S. The Mathematica produces the following output for this sum:
>
>
>           n   1 1 + n
> Out[1]= p  ((-)      (-1 + 2 p) -
>               p
>
>                1 Ceiling[n/2]
>  >      ((-1 + -)             (-1 + p) Gamma[1 + n]
>                p
>
>                                       n
>  >         ((1 + n) Gamma[n - Ceiling[-]]
>                                       2
>
>                                                 n               n   -1 + p
>  >            Hypergeometric2F1[1, -n + Ceiling[-], 2 +
Ceiling[-], ------] -
>                                                 2               2     p
>
>                                      n
>  >           2 Gamma[1 + n - Ceiling[-]]
>                                      2
>
>                                                    n               n   -1
+ p
>  >            Hypergeometric2F1[1, 1 - n + Ceiling[-], 2 +
Ceiling[-], ------])
>                                                    2               2     p
>
>                                     n                         n
>  >         ) / (p Gamma[n - Ceiling[-]] Gamma[1 + n - Ceiling[-]]
>                                     2                         2
>
>                              n
>  >         Gamma[2 + Ceiling[-]]))
>                              2
>
>
>
>
>
>
>
> Constantine Elster
> Computer Science Dept.
> Technion I.I.T.
> Office: Taub 411
> Tel: +972 4 8294375
>




  • Prev by Date: Re: Lists and tables
  • Next by Date: Re: Trying to solve a sum
  • Previous by thread: Trying to solve a sum
  • Next by thread: Re: Trying to solve a sum