%e

From the Maxima mailing list today:
(%i4) load("simplify_sum")$

(%i5) simplify_sum(sum(1/n!,n,0,inf));
(%o5) %e

Someone had noted that sum(1/n!,n,0,inf),simpsum; wasn't evaluating to %e.

Someone else pointed out

(%i6) taylor(%e^n, n, 0, 6);
                            2    3    4    5     6
                           n    n    n    n     n
(%o6)/T/           1 + n + -- + -- + -- + --- + --- + . . .
                           2    6    24   120   720

What else does Maxima know?

(%i8) sum(k, k, 1, n), simpsum;
                                     2
                                    n  + n
(%o8)                               ------
                                      2
...
(%i10) simplify_sum(sum((-1)^(k+1) / k, k, 1, inf));
                          - 2 log(2) - %gamma   %gamma
(%o10)                  - ------------------- - ------
                                   2              2
(%i11) ratsimp(%);
(%o11)                              log(2)
(%i12) simplify_sum(sum(1/k^2, k, 1, inf));
                                        2
                                     %pi
(%o12)                               ----
                                      6
(%i13) simplify_sum(sum(1/k^3, k, 1, inf));
(%o13)                              zeta(3)
...
(%i17) simplify_sum(sum(4^(-k) * z^(2*k)/(k!)^2, k, 0, inf));
                                 inf
                                 ====    2 k
                                 \      z
(%o17)                            >    ------
                                 /      k   2
                                 ====  4  k!
                                 k = 0
... No Bessel functions?
(%i19) simplify_sum(sum(1/k^10, k, 1, inf));
                                        10
                                     %pi
(%o19)                               -----
                                     93555
(%i20) simplify_sum(sum(1/k^50, k, 1, inf));
                                                     50
                       39604576419286371856998202 %pi
(%o20)        ---------------------------------------------------
              285258771457546764463363635252374414183254365234375
...
(%i22) simplify_sum(sum(1/(k^2 + 1), k, 1, inf));
                       %i psi (1 - %i)   %i psi (%i + 1)
                             0                 0
(%o22)                 --------------- - ---------------
                              2                 2
... What is this?