Dini condition

Dini condition [′dē·nē kən¦didh·ən]

(mathematics)

A condition for the convergence of a Fourier series of a function ƒ at a numberx, namely, that the limits of ƒ atxon the left and right, ƒ (x-) and ƒ (x+), both exist, and that the function given by the absolute value of [ƒ(x+t) - ƒ (x+) + ƒ (x-t) - ƒ (x-)]/tbe integrable on some closed interval, -d≤t≤d, wheredis a positive number.