Differentiable Even Functions
An even function f (x) = f (−x) (defined in a neighborhood of the origin) can be expressed as a function g(x 2); g(u) is determined for u ≥ 0, but not for u < 0. We wish to show that g may be defined for u < 0 also, so that it has roughly half as many derivatives as f. A similar result for odd functions is given.
- 3.H. Whitney, Differentiability of the remainder term in Taylor’s formula, this Journal, vol. 10 (1943), pp. 153–158.Google Scholar