  The order derivatives of the modified Bessel function of the second kind at s
= .5 are obtained as finite expressions of integrals that generalize the
exponential integral appearing in the first derivative (Theorem 1.) The
derivatives arise in the investigation of a BesselK relationship with the
Riemann zeta function. Any use of the term, derivative, with respect to a
Bessel function, here means a derivative with respect to its order.
