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:
“No one is without Christianity, if we agree on what we mean by that word. It is every individual’s individual code of behavior by means of which he makes himself a better human being than his nature wants to be, if he followed his nature only. Whatever its symbol—cross or crescent or whatever—that symbol is man’s reminder of his duty inside the human race.”
—William Faulkner (1897–1962)