Delta Functions

Implementation of the Kronecker delta and Dirac delta functions

This module implements the following methods:

• kronecker_delta(i, j): Discrete analog of Dirac delta function δij for integers i and j

• dirac_delta(x): Dirac delta function δ(x) defined along the real number line:

• dirac_delta_integral(lowerBound, upperBound): Integral of the Dirac delta function: ∫ δ(x) dx from lowerBound to upperBound

  (Returns the indefinite integral from -∞ to +∞ when no arguments given)

• nascent-delta(a, x): Evaluates ηa(x), a function within a sequence of zero-centered normal distributions

• nascent-delta-integral(a, lowerBound, upperBound) : Integral of the nascent delta function: ∫ η(x) dx from lowerBound to upperBound

  (Returns the indefinite integral from -∞ to +∞ when no arguments given)

See Wikipedia for details.