||paper by Wong et al.  compares eight different methods just for the k = 1/2 case. Their paper showed a great variation in accuracy and efficiency between the various methods.
While several methods for computing 3^(x) have been proposed, there seems to be little available software for these functions. The paper by Banuelos et al.  describes a code using a mixture of power series, continued fractions, and asymptotic series, but giving only a relative accuracy of 10~5. The code of Fullerton and Rinker  gives a relative accuracy of 10~10 by using a method of quadrature followed by piecewise fitting of Chebyshev polynomials. Both these codes are for general k. According to Lozier and Olver , the CERNLIB package contains codes. On investigating the CERNLIB information available through the Internet, it seems that these codes implement the rational approximations derived by Cody and Thacher . Unfortunately, these codes are not free. Very recently, Goano  has developed a method for the incomplete Fermi-Dirac integral