The maximum value, which occurs at x = 0, is \(1/ \sqrt{ \pi} = 0.5642\), and it is easy to show that the half width at half the maximum is \( \sqrt{ \ln 2} = 0.8326\). Also of some interest (though n...The maximum value, which occurs at x = 0, is \(1/ \sqrt{ \pi} = 0.5642\), and it is easy to show that the half width at half the maximum is \( \sqrt{ \ln 2} = 0.8326\). Also of some interest (though not particularly in this chapter) is the square root of the second moment of area around the y-axis. The area outside the limits x = ±a, which is the area under the two “tails” of the gaussian function, is sometimes called the complementary error function:
