Exponentiation
When it is a positive integer, the exponent indicates how many copies of the base are multiplied together. For example, . The base appears times in the repeated multiplication, because the exponent is . Here, is the "base", is the "exponent", and is the "power" or, more specifically, "3 raised to the 5th power".
Exponential smoothing
The use of the exponential window function is first attributed to Poisson as an extension of a numerical analysis technique from the 17th century, and later adopted by the signal processing community in the 1940s. Here, exponential smoothing is the application of the exponential, or Poisson, window function. Exponential smoothing was first suggested in the statistical literature without citation to previous work by Robert Goodell Brown in 1956, and then expanded by Charles C. Holt in 1957. The formulation below, which is the one commonly used, is attributed to Brown and is known as “Brown’s simple exponential smoothing”. All the methods of Holt, Winters and Brown may be seen as a simple application of recursive filtering, first found in the 1940s to convert FIR filters to IIR filters.