# More on the Kronecker Delta and Fourier Series

Standard

Modified my spreadsheet to sum the integral. So here is $\int_{-\pi}^{\pi}sin(mx)sin(ny)$ and $sin(mx)sin(nx)$ with $m = n$. (Integral is the dark orange line)

And for $n = 5m$

And for $n = 2.1m$:

sin(x)sin(y) with integral where y = 2.1x

So, it’s pretty clear $\delta_{mn}$ (the Kronecker delta) applies when both $m$ and $n$ are integers.