Standard and Less Standard Asymptotic Methods - Lecture 8

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. Examine practical examples, including 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. Cover topics such as optimal truncation, smooth truncation, optimal smooth truncation, and applications to the Gamma function. Gain insights into advanced mathematical problem-solving techniques applicable across various branches of mathematics.