bit of editing wanted : are these equivalent?
wouter meeussen
wouter.meeussen at pandora.be
Sun Dec 7 13:18:06 CET 2003
a spot of trouble:
both my
Numerators of Series[1/(1 + Cosh[Sqrt[x]]), {x, 0, 24}]
and Benoit's
Numerators of ... 2/(exp(x)+1)
are equivalent,
but DIFFERENT from
Numerators of Table[2*BernoulliB[2*n]*(4^n - 1)/(2*n), {n, 25}]
that, (saving Benoit's day), correctly gives the
Denominators of Pi^(2n)/(Gamma[2n]*(1 - 2^(-2n))*Zeta[2n])
Close, but no cigar,
'cause the ratios between latter and former are:
{1,1,1,1,1,1,1,1,1,1,1,17,1,1,1,1,1,1,1,527,1,1,1,1,31}
differences for n= 11,19 and 24 (offset 0)
does that ring a Bell?
a Bernoulli-effect?
W.
----- Original Message -----
From: "Brendan McKay" <bdm at cs.anu.edu.au>
To: <seqfan at ext.jussieu.fr>
Sent: Saturday, December 06, 2003 11:03 PM
Subject: Re: bit of editing wanted : are these equivalent?
> * benoit <abcloitre at wanadoo.fr> [031207 08:56]:
> >
> > Yes that's an interesting equivalence. Let (A(n)) having g.f.
> > x/(1+cosh(x)) and (B(n)) having g.f. 2/(1+exp(x))
> >
> > then A(n)+n*B(n)=0
>
> x times the derivative of 2/(1+exp(x)) is the negative of x/(1+cosh(x)),
> that's all.
>
> B.
>
>
>
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