4
$\begingroup$

This problem came from the Krantz text ($2^{nd}$ ed. ch. 9, prob. 17): Prove that the series $\displaystyle\sum_{j=1}^{\infty }{\frac{\sin{(jx)}}{j}}$ converges uniformly on compact intervals that do not contain odd multiples of $\displaystyle\frac{\pi}{2}$

Thank you in advance for your help

  • 5
    Hmmm, are you sure is for odd multiples of $\frac{\pi}{2}$? This is the Fourier series for the sawtooth function, which is discontinuous at $x=0$, so this series cannot converge uniformly on any interval containing $0$.2011-08-31

0 Answers 0