A strange coincidence which I discovered recently, is that
$$\int_{-\infty}^{\infty}{\tan^{-1}{\frac{1}{(x-\alpha)^2+\frac{3}{4}}}}dx = \sum_{x=-\infty}^{\infty}{\tan^{-1}{\frac{1}{(x-\alpha)^2+\frac{3}{4}}}}$$
Are there any other functions for which this characteristic holds true, and if so, what do they all have in common, and how can we determine them (if possible)?
Sunday, 13 December 2015
sequences and series - Identical Summation and Integration of specific functions
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment