Standard and Less Standard Asymptotic Methods - Lecture 9

Explore advanced asymptotic methods in mathematics through this SISSA/IGAP lecture. Delve into techniques for evaluating infinite sums numerically and recognizing asymptotic patterns in number sequences. Learn both standard approaches like the Euler-Maclaurin formula and less conventional methods, illustrated with diverse examples. Examine challenging problems such as evaluating a slowly convergent sum to high precision, analyzing the asymptotic behavior of complex series coefficients, and computing highly oscillatory infinite series. Gain insights into the circle method, Euler's key point, Hardy-Ramanujan techniques, and generalized asymptotics. Discover transformations, variable changes, and simplification strategies for tackling complex mathematical problems in various branches of mathematics.

Intro
The circle method
Fabio Novias
Euler
Key point
Hardy Ramanujan
Squares
Transformation behavior
Generalized asymptotics
Finding asymptotics
Changing variables
The second simplification