TOPICS
Search

Dini's Test

A test for the convergence of Fourier series. Let

phi_x(t)=f(x+t)+f(x-t)-2f(x),

then if

int_0^pi(|phi_x(t)|dt)/t

is finite, the Fourier series converges to f(x) at x.

See also

Fourier Series

Explore with Wolfram|Alpha

References

Sansone, G. Orthogonal Functions, rev. English ed. New York: Dover, pp. 65-68, 1991.

Referenced on Wolfram|Alpha

Dini's Test

Cite this as:

Weisstein, Eric W. "Dini's Test." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DinisTest.html

Subject classifications