Asymptotic Behavior
The asymptotic behavior of U(a,b,z) as z → ∞ can be deduced from the integral representations. If z = x is real, then making a change of variables in the integral followed by expanding the binomial series and integrating it formally term by term gives rise to an asymptotic series expansion, valid as x → ∞:
where is a generalized hypergeometric series, which converges nowhere but exists as a formal power series in 1/x.
Read more about this topic: Confluent Hypergeometric Function
Famous quotes containing the word behavior:
“There is a parallel between the twos and the tens. Tens are trying to test their abilities again, sizing up and experimenting to discover how to fit in. They don’t mean everything they do and say. They are just testing. . . . Take a good deal of your daughter’s behavior with a grain of salt. Try to handle the really outrageous as matter-of-factly as you would a mistake in grammar or spelling.”
—Stella Chess (20th century)