DHB: Could you provide some details?  Why do you say the functions are in the BBP class? WDS: My aim was to make the coefficient of x^n in their Maclaurin series be a rational function of n with integer coefficients. Such functions are in BBP class. Unless I screwed up, this ought to be provable inductively and I thought was pretty obvious? Ummm. Oh dear. Actually, I think I *did* screw up: when I said "rational-fn linear combinations" I should have demanded that all the rational functions of x we use need to be chosen so their poles (if any) all are located on the perimeter of the unit circle (which they were in my first definition). You want coeff[n] to be rational(n) -- not to also have exponential(n) dependence, which would happen if poles located on other-radius circles. By the way,I just thought of a slight further extension: if F(x) is in BBP class, then so is F(x^Q) for any positive integer Q (since a number written in radix 1000 is also a number written in radix 10) and we can put this into the inductive definition too.