Standard and Less Standard Asymptotic Methods - Lecture 6

Explore advanced asymptotic methods in mathematics through this lecture on "Standard and less standard asymptotic methods." Delve into techniques for evaluating infinite sums numerically, guessing exact values, and recognizing asymptotic laws of number sequences. Learn about both standard approaches like the Euler-Maclaurin formula and less conventional methods, illustrated with numerous examples. Examine challenging problems such as evaluating a slowly convergent sum to 250 decimal digits, analyzing the asymptotic behavior of coefficients in an infinite sum expansion, and computing a highly oscillatory series for large real numbers. Gain insights into exponential functions, Bell numbers, and dedicated data functions as you enhance your understanding of complex mathematical concepts and problem-solving strategies.

Introduction
Example
Exponential functions
Bell numbers
An example
Dedicated data function