In many other cases we were not able to obtain a formula for the Euler
sum constant explicitly in terms of values of the Riemann zeta,
logarithm and polylogarithm functions, but we were able to obtain
relations involving two or more Euler sum constants of the same degree
(where by ``degree'' we mean m + n, where m and n are the
indices of the constant). Some of these relations are shown in
Table 3. This is not a complete list; we have obtained numerous other
relations of this type. The ``confidence level'' of each of these
relations is smaller than . The uniqueness of each of these
relations was checked by repeating the run with one fewer constant
input to PSLQ (there should be no relation detected when this is
done).
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