"However, under certain conditions, such as when f and g are both analytic functions and f is positive on the open interval (0, b) for some positive b, the limit approaching from the right is always 1.[26][27][28]"
Also, definitely take note of Knuth's argument, because while you might feel strongly that indeterminate is the right answer right now, there are big implications for allowing other choices. (And NB: indeterminate vs undefined)
"The debate stopped there, apparently with the conclusion that 0^0 should be undefined.
But no, no, ten thousand times no! Anybody who wants the binomial theorem to hold for at least one nonnegative integer n must believe that 0^0 = 1, for we can plug in x = 0
and y=1 to get 1 on the left and 0^0 on the right.
The number of mappings from the empty set to the empty set is 0^0. It has to be 1."
https://en.m.wikipedia.org/wiki/Exponentiation#Continuous_ex...
With the caveat:
"However, under certain conditions, such as when f and g are both analytic functions and f is positive on the open interval (0, b) for some positive b, the limit approaching from the right is always 1.[26][27][28]"
Also, definitely take note of Knuth's argument, because while you might feel strongly that indeterminate is the right answer right now, there are big implications for allowing other choices. (And NB: indeterminate vs undefined)
"The debate stopped there, apparently with the conclusion that 0^0 should be undefined.
But no, no, ten thousand times no! Anybody who wants the binomial theorem to hold for at least one nonnegative integer n must believe that 0^0 = 1, for we can plug in x = 0 and y=1 to get 1 on the left and 0^0 on the right. The number of mappings from the empty set to the empty set is 0^0. It has to be 1."
http://arxiv.org/pdf/math/9205211v1.pdf