The k-th derivative of this function is negative one to the k times the k-th derivative of test functions phi evaluated at zero. For a non-zero scalar alpha, this function of alpha-x equals this function of x divided by the magnitude of alpha. The convolution of this function with any other tempered distribution S is S since its Fourier transform is 1. Applying (-5[1])an operator to its associated (15[1])(*) Green’s function gives this distribution. This distribution’s sifting property integrates (10[1])over all space and will return another function’s evaluation where this distribution is centered. This distribution is the derivative of the Heaviside step function and is the limit of a Gaussian as it gets taller and thinner. (10[1])For 10 points, name this distribution which is zero everywhere except at the origin, where it is infinite. ■END■