| 释义 |
analytic A function is analytic if it can be defined by a convergent Taylor series in a neighbourhood of any point of the domain. An analytic function necessarily has derivatives of all orders, but the converse is not true. The real function, defined by f(x) = exp(−1/x2) for x ≠ 0 and f(0) = 0, is infinitely differentiable at x = 0, with all derivatives being 0; thus, the Taylor series at x = 0 only converges to the function at 0. The space of analytic functions is denoted Cω.
|