# Weierstrass' nondifferentiable function

Weierstrass' nondifferentiable function is the earliest known example of a **pathological function** –
a function that gives rise to a pathological
curve. It was investigated by Karl Weierstrass,
but had been first discovered by Bernhard Riemann,
and is defined as:

where 0 < *a* < 1, *b* is a positive odd integer, and ab >
1 + 3π/2.

The Weierstrass function is everywhere continuous but nowhere differentiable; in other words, no tangent exists to its curve at any point. Constructed from an infinite sum of trigonometric functions, it is the densely-nested oscillating structure that makes the definition of a tangent line impossible.