- Thread starter
- #1
DreamWeaver
Well-known member
- Sep 16, 2013
- 337
This thread is dedicated to the study of Log-Trig series of the form:
\(\displaystyle \mathscr{S}_{(m, n)} (z) = \sum_{k=1}^{\infty}\frac{(\log k)^m}{k^n}\, \sin 2\pi k z\)
\(\displaystyle \mathscr{C}_{(m, n)} (z) = \sum_{k=1}^{\infty}\frac{(\log k)^m}{k^n}\, \cos 2\pi k z\)
Where \(\displaystyle m, n \in \mathbb{Z} \ge 1\), and \(\displaystyle 0 < z < 1 \in \mathbb{Q}\).
This is NOT a tutorial, so by all means DO chime in, if it tickles yer fancy...
\(\displaystyle \mathscr{S}_{(m, n)} (z) = \sum_{k=1}^{\infty}\frac{(\log k)^m}{k^n}\, \sin 2\pi k z\)
\(\displaystyle \mathscr{C}_{(m, n)} (z) = \sum_{k=1}^{\infty}\frac{(\log k)^m}{k^n}\, \cos 2\pi k z\)
Where \(\displaystyle m, n \in \mathbb{Z} \ge 1\), and \(\displaystyle 0 < z < 1 \in \mathbb{Q}\).
This is NOT a tutorial, so by all means DO chime in, if it tickles yer fancy...