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
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