This is an example of an asymptotic expansion.

He is known for pioneering work in applying the method of asymptotic expansion to fluid mechanics problems.

The most common type of asymptotic expansion is a power series in either positive or negative terms.

Repeated integration by parts will often lead to an asymptotic expansion.

Substituting and noting that results in the asymptotic expansion given earlier in this article.

It is typical that the accuracy of asymptotic expansions grows with localization.

The general case can be solved approximately by means of an asymptotic expansion in the parameter .

Bernoulli numbers are also frequently used in other kinds of asymptotic expansions.

They were studied by , who found asymptotic expansion for their coefficients, and in .

In general the power series will not converge but will provide only an asymptotic expansion of the exact solution.