This site will archive some Stieltjes-related computational
work, soon - not just
my own, but hopefully other relevant work too.
For now, the following links to just my own work may be useful:
- Computations of Taylor coefficient values for ξ
(the
\xi function) at s=1/2 - unpublished graphics; preprint coming soon
- numerical values that were
plotted in graphics above (formatted as output of a Mathematica
function) - these values,
from 2003, are to much less precision than subsequent
computations, i.e. if high-precision numerics
are needed the values linked to below should be used.
- Further computations of s=1/2 Taylor
coefficient values for ξ through 2k=1000; AND σk values for
k=1 to 2040 - and Taylor
computations for ξ at s=1 for k=1 to 1400 - along with unpublished
graphics; preprint coming soon
- High-precision numerical values as depicted in graphics above
are available at the following links in the form
of output of a Mathematica function. Precision various
from several thousand digits of accuracy to just over 20 digits
of accuracy. Once ported in to Mathematica, all
digits depicted are exact except last digit is rounded. These
numerical results are currently
unpublished. Computations were undertaken in late September
and early October 2005, for σk and ξ's derivatives
at s=1/2,
then some were re-checked in early December 2005, along
with computations for ξ's derivatives at s=1: ξ derivative values
for first 1000 derivatives at s=1/2; σk
values for k=1
to
2040; and ξ derivative values
for first 1400 derivatives at s=1.
- Newton-Cotes
integration for approximating Stieltjes (generalized Euler) constants
from Mathematics of Computation,72 (2003), 1379-1397
- supplemental
info related to this paper - "g"
(some aspects of the function g are explored in greater detail;
in particular, computational a values that yield optimal Ck(a)
as k varies are plotted,
and also directly available here)
- supplemental info related to this paper - Ck(a)
,
namely unpublished plots of Ck(a), for fixed k,
as a varies
- Values of Ck(a) and γk(a)
for k=1,2,...,1000 to 400 digits for a=1/3, 2/3 and 1
are available here as a Mathematica
file. There are five tables
in the file, namely truetable13ghk for γk(1/3),
truetable23ghk for γk(2/3),
truetable33ghk for γk(1),
truetable13ck for Ck(1/3), and
truetable23ck for Ck(2/3). [Similarly,
values of Ck(a) and γk(a)
for k=1,2,...,1000 to 400 digits for a=5/6 (i.e. a=1/3+1/2)
are available here as a Mathematica
file. There are two tables
in the file, namely truetable56ghk for γk(5/6) and
truetable56ck for γk(2/3).]
- Values of Stieltjes constants
γ1 to γ10000 to
varying degrees of precision (e.g. thousands are available
to several thousand digits) are available upon request.
As illustration, values of γ1 to γ12 to
6900 digits are available for immediate download here;
and high-precision values for γ20000, γ25000,
..., γ45000 and γ50000 are available in a text
file here.
γ100 and γ101, to 11111 digits each, are available
here.
- Follow these links to unpublished plots related to values of
coefficients related
to the Riemann zeta function and the Riemann hypothesis
(denoted τk and λk);
a different plot of λk; and
high-precision values of λk,
for
k=1 to 2001. The precision values were computed in late September
and early October 2005.
Rick
Kreminski, March 2004
Under construction!