FOM: nowhere differentiable/natural

Martin Davis martin at
Thu Aug 5 19:37:26 EDT 1999

At 03:12 PM 8/5/99 -0700, Martin Davis wrote:

>I don't see anything "unnatural" about Weierstrass's original example:
>             SUM[0 to infinity] [b^n cos(a^n \pi x)]
>Here 0<b<1 and a is an odd positive integer. (Titchmarsh, THEORY OF
>FUNCTIONS, p.351.)
I should have added the condition ab > 1. (Tichmarsh only deals with the case
ab > 1 + 3\pi/2)

                           Martin Davis
                   Visiting Scholar UC Berkeley
                     Professor Emeritus, NYU
                         martin at
                         (Add 1 and get 0)

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