Дигамма-функция. Часть2. Интегральные представления и разложение в ряд

In this video, we will continue to get acquainted with the digamma function and derive basic formulas: we will obtain several integral representations for it, a series expansion, and also some particular values. This is the 2nd video of 2 about the digamma function, which are related to each other. This is the 1st video about the digamma function:    • Дигамма-функция. Часть1. Функциональные ур...   Here is the integral of ((e^(-x)-e^(-t*x))/x, which was used in the video:    • Несобственный интеграл (e^(-x)-e^(-2x))/x....   In this video, when finding the integral, an integral representation for harmonic numbers was obtained:    • Будь гармоничным, как интеграл!   And this is a video about the gamma function:    • Гамма-функция и бета-функция: вывод основн...   If you have the opportunity, support the channel: sberbank: 4276160020048840 tinkoff: 5536914075973911 regular support: https://boosty.to/hmath