The Weierstrass Nowhere Differentiable Function
We construct a family of functions depending on two parameters that are everywhere continuous but nowhere differentiable. These functions are all lucunary Fourier series whose oscillation grows more rapidly than its modes decay. We use the Weierstrass M-Test to prove that the series converges to a continuous function. We carefully choose a sequence of values tending to zero on which the difference quotient grows exponentially.
#mikethemathematician, #mikedabkowski, #profdabkowski
Watch video The Weierstrass Nowhere Differentiable Function online without registration, duration hours minute second in high quality. This video was added by user Mike, the Mathematician 31 August 2024, don't forget to share it with your friends and acquaintances, it has been viewed on our site 260 once and liked it 14 people.