Unpublished work:
I arrived at these value, for derivatives of ξ at s=1/2, indirectly.  As a result of this indirect approach, I lost precision, and thus only supply the values of the 2kth derivatives of ξ at s=1/2 for 2k from 2 to 490 at this time.  

My indirect approach: I found the Taylor series coefficients for / ξ centered at s=1, then took the antiderivative to get the series for log(ξ) centered at s=1, then recentered to s=1/2, then used the coefficients, which were values of the derivatives of log(ξ) at s=1/2, to obtain the values of the derivative of the exponential, i.e. of ξ, at s=1/2.  As a partial test, I used the 490 coefficients to estimate values of ξ at various values of s; e.g. for s=3/4 + 10I, the series was accurate to approximately 540 digits.

Actual values are stored in the file "xiderest"

Rick Kreminski
November 10, 2003