Chapter 5 uses the Riemann Weirstrauss function as an example.

Google keywords "differentiability Riemann function 1971"

http://mathworld.wolfram.com/WeierstrassFunction.html

Note the web page must really mean absolute value of the derivative, since it is clearly negative at x = 1, so if the slope of this function is -1/2, then we must multiply by Pi to get our function slope since the functions are defined by a missing factor of Pi... to get -Pi/2 about -1.57!

The second hit is a really interesting article at the AMS:

http://www.ams.org/tran/2003-355-11/S0002-9947-03-03149-0/home.html

You will see that the sine and corresponding cosine series used in chapter 5 are
just the imaginary and real parts of the complex exponential series studied in
this AMS article:

> Sum(exp(n^2*Pi*x) /n^2,n=1..infinity);