Re: Bernoulli Numbers
- To: mathgroup at smc.vnet.net
- Subject: [mg122624] Re: Bernoulli Numbers
- From: Bob Hanlon <hanlonr357 at gmail.com>
- Date: Thu, 3 Nov 2011 03:48:50 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201111021122.GAA03586@smc.vnet.net>
Clear[b];
b[0] = 1;
b[n_Integer?Positive] := b[n] = (x /. Solve[
Sum[Binomial[n + 1, k]*b[k], {k, 0, n - 1}] + (n + 1)*x == 0,
x][[1]])
And @@ Table[b[n] == BernoulliB[n], {n, 0, 20}]
True
Sum[Binomial[21, k]*b[k], {k, 0, 20}] == 0
True
Table[{n, b[n]}, {n, 0, 20}] // Grid
Bob Hanlon
On Wed, Nov 2, 2011 at 7:22 AM, David Turner <DTurner at faulkner.edu> wrote:
> Hello,
>
> I wish to compute several Bernoulli numbers, say B0 through B20. The Bernoulli numbers are defined recursively by
>
> B0 = 1, and Solve[Sum[Binomial[n,k]*Bk,{k,0,n-1}]==0,Bn-1] for n > 1
>
> I am trying to compute these numbers in some type of loop, and display them in a table. Any help is greatly appreciated.
>
> Thanks,
>
> David
- References:
- Bernoulli Numbers
- From: David Turner <DTurner@faulkner.edu>
- Bernoulli Numbers