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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



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