One of a collection of cubic polynomials used in interpolating a function whose value is specified at each of a collection of distinct ordered values, X_i (i =1, ..., n ), and whose slope is specified at X₁ and X_n; one cubic polynomial is found for each interval, such that the interpolating system has the prescribed values at each of the X_i , the prescribed slope at X₁ and X_n , and a continuous slope at each of the X_i .