بوتار ِ دیریکله butâr-e Dirichlet
*Fr.: condition de Dirichlet*
One of the following conditions for a → *Fourier series*
to converge:
1) The function *f(x)* is defined and single valued, except possibly at a finite number of
points in the interval -π, +π.
2) *f(x)* has a period of 2π.
3) *f(x)* and *f'(x)* are
→ *piecewise continuous function*s on -π, +π.
Then, the Fourier series converges to:
(a) *f(x)* if *x* is a point of continuity.
(b) *(f(x + 0) + f(x - 0))*/2, if *x* is a point of discontinuity. Named after Peter Gustav Lejeune Dirichlet (1805-1859), German mathematician who
made valuable contributions to → *number theory*,
→ *analysis*, and → *mechanics*;
→ *condition*. |