Re: Rational approximations to gamma

Rob Johnson wrote:

In article <6e0ca$46d56a7b$82a1e228$25379@xxxxxxxxxxxxxxxx>,
Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:

Rob Johnson wrote:

Note that AHT(2^k) is less than 1/2^k, so the series in [5] converges
geometrically. Similarly, the series in [6] converges geometrically.

Does this answer your questions?

Almost. Does the series in [6] converge faster than the series in [5] ?
(At first sight, it appears that they should give an identical outcome)


Asymptotically, the reciprocal of the terms in [5] are 2^{k+1}. When
j is much greater than m, the reciprocal of the terms in [6] are about
2^j j^{m+1}/m!. Both of these series have term to term ratios that
approach 1/2, but the series in [6] does converge a bit faster.

Thank you very much for these posters! (Seems to be more handsome than
working with Bernoulli numbers .. No?)

Although I am sure there are ways to compute gamma that converge much
faster, this one is very elementary at least. It is very easy to
program as well.

Affirmative. Thanks again:

Han de Bruijn

.