fast accurate Kneser sexp algorithm
Another small update. I added "slogtaylor(w,r)" to generate the slog taylor series, centered at "w", generated with a sample radius of "r". For sexp, there is the sexptaylor(w,r) function. I also speed up the slog(z,est) routine, where "est" is an optional initial estimate. Both the sexptaylor/slogtaylor series can be centered anywhere in the complex plane, but I rounded to a real valued Taylor series if imag(w)=0, at the real axis. update Jan 6th, 2011. fix for base B>=500, which I had accidentally broken with my slog routine updates

June 3rd 2011 update:, added support for base eta, which is a separate function. New functions, cheta(z), sexpeta(z), invcheta(z), invsexpeta(z), which generate the superfunctions and inverse superfunctions for base \( \eta=\exp(1/e) \). The default precision for these new functions is approximately 50 decimal digits of accuracy, with "\p 67" as the default precision setting, and 120 decimal digits accuracy with the "\p 134" setting.
- Sheldon

.gp (Size: 35.15 KB / Downloads: 1,005) June 2011 version, with \( \text{sexp}_\eta(z) \) support, update, fixed typo in slog
For the most recent code version: go to the Nov 21st, 2011 thread.

Messages In This Thread
The pari-GP code - by sheldonison - 08/07/2010, 09:17 PM
updated code - by sheldonison - 08/19/2010, 02:35 AM
RE: updated code - by nuninho1980 - 08/19/2010, 12:08 PM
RE: updated code - by sheldonison - 08/20/2010, 01:05 AM
update to support B<eta - by sheldonison - 11/15/2010, 02:53 PM
RE: update to support B<eta - by nuninho1980 - 11/15/2010, 03:26 PM
another new version - by sheldonison - 11/17/2010, 06:52 PM
RE: fast accurate Kneser sexp algorithm - by sheldonison - 12/26/2010, 12:35 PM

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