Input

ℱ_t[1](ω)

Result

1/sqrt(2 π) integral_(-∞)^∞ 1 e^(i ω t) dt = sqrt(2 π) δ(ω)

Alternate form assuming ω>0

0

Trigonometric transform

ℱ_t[1](ω) = ℱ_t^c[1](ω)

Fourier cosine transform for the even part

sqrt(2/π) integral_0^∞ 1 cos(ω t) dt = sqrt(2 π) δ(ω)