Double factorials can also be used to evaluate integrals of more complicated trigonometric polynomials. Similarly, factorials can be approximated by summing the logarithms of the terms. Falling factorials define, up to scaling, the same polynomials as binomial coefficients&colon; formula 19. Thus many identities on binomial coefficients carry over to the falling and rising factorials. Note, however, that the hypergeometric function literature uses the notation formula 25 for rising factorials. The sum over "s" is over such values that the factorials are nonnegative. Most software applications will compute small factorials by direct multiplication or table lookup. In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials. The example below is used to compute factorials. There is a variation of Borel summation that replaces factorials "n"! The calculation of factorials can easily produce very large numbers. Therefore, the factorials do not form an irrationality sequence. It is also the sum of the squares of the factorials of 2,3,4. It is similar to the descriptions of factorials found in mathematics textbooks. The main practical difficulty in computing factorials is the size of the result.