The value of a Fourier series at a jump point (discontinuity)

[Amaelle]

Homework Statement

calculate the value of the fourier serie at x=e for the e periodic function (0,e]
f(x)=log(x)

Relevant Equations

Fourier serie

Greetings
according to the function we can see that there is a jump at x=e and I know that the value of the function at x=e should be the average between the value of f(x) at this points
my problem is the following
the limit of f(x) at x=e is -infinity and f(e)=1
how can we deal with such situations?

thank you!

 

[LCKurtz]

Since $f(0^+) = -\infty$, your function doesn't satisfy the Dirichlet conditions, so the usual theorem about convergence doesn't apply.

 

[Amaelle]

Since $f(0^+) = -\infty$, your function doesn't satisfy the Dirichlet conditions, so the usual theorem about convergence doesn't apply.

thanks a million!