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Brian R. Hunt

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Proc. Amer. Math. Soc. 126 (1998), 791-800.
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The Weierstrass nowhere differentiable function, and functions
constructed from similar infinite series, have been studied often as
examples of functions whose graph is a fractal. Though there is a
simple formula for the Hausdorff dimension of the graph which is
widely accepted, it has not been rigorously proved to hold.
We prove that if arbitrary phases are included in each term of the
summation for the Weierstrass function, the Hausdorff dimension of the
graph of the function has the conjectured value for almost every
sequence of phases. The argument extends to a much wider class of
Weierstrass-like functions.

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