I read in my text book that the Dirichlet conditions are sufficient conditions for a real-valued, periodic function $f(x)$ to be equal to the sum of its Fourier series at each point where $f$ is continuous.
However, it further stated that although the conditions are sufficient but they are NOT necessary.
Why are the Dirichlet conditions "not necessary" ?
Example : One of the Dirichlet conditions state that the function can not have infinite discontinuities. Hence we can not express, a function like $ tan x $ in terms of a Fourier series since (as it appears) violates one of the conditions. So, why is that they are 'not necessary'?
P.S.: The Wikipedia Link to the Dirichlet conditions.