Chapter 5 uses the Riemann Weirstrauss function as an example.

Google keywords "differentiability Riemann function 1971"

Google search

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:


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);