I saw this sum somewhere as a question as to whether it has a closed form. I am pretty sure it doesn't have any elementary closed form, but I'd think that this isn't a whole new class of functions (with respect to special functions). (%i1) 'sum(1/(x^k + k!), k, 0, inf); inf ==== \ 1 (%o1) > ------- / k ==== x + k! k = 0 for some real x (we might even just consider positive integral x). Maybe even just (%i2) 'sum(1/(1 + k!), k, 0, inf); inf ==== \ 1 (%o2) > ------ / k! + 1 ==== k = 0 Can we write this in any other useful forms? (cue the Gosperfunctionology) -Robert