This approximation can be obtained by using the binomial theorem and ignoring the terms beyond the first two.
The left-hand side of this relation is always greater than or equal to the right-hand side for and a non-negative integer, by Bernoulli's inequality.
Derivation using linear approximation
When x = 0:
Using linear approximation:
Derivation using Mellin transform
Using the inverse Mellin transform:
Closing this integral to the left, which converges for , we get: