  Whereas the Dirac delta function introduced by P. A. M. Dirac in 1930 in his
famous quantum mechanics text has been well studied, a not famous formula
related to the delta function using the Heaviside step function in a
single-variable form, also given in Dirac's text, has been poorly studied. We
demonstrate the decomposition of a nonlinear multivariate function into a sum
of integrals in which each integrand is composed of a derivative of the
function and a direct product of Heaviside step functions. It is an extension
of Dirac's single-variable form to that for multiple variables. Moreover, it
remains mathematically equivalent to the definition of the Dirac delta function
with multiple variables, and offers a mathematically unified expression.
