James Arathoon

Hertfordshire, United Kingdom

Control and Automation Engineer

Main Mathematical Interests:

Integration, Infinite Series and Elementary Number Theory.

One particular interest is finding new Infinite Series for Apéry's Constant and other Zeta Constants e.g. this especially strange one I found for Apéry's Constant last year (2016),

$$\zeta(3)=$$ $$\frac{1}{2}\frac{8}{7} \left(\frac{\pi}{2}\right)^3 \left(\frac{\pi}{4}\right)^3 \left( b_{1} \lvert B_{4}\rvert + b_{2} \lvert B_{6} \rvert \left(\frac{\pi}{4}\right)^2 + b_{3} \lvert B_{8} \rvert \left(\frac{\pi}{4}\right)^4+ \; ... \right)$$

where $ b_k=\left( \frac{2^{2k+2}\left( 2^{2k+2}-1\right)\left( 2^{2k+1}-\left( k+2\right)\right)}{\left( 2k+2\right)! \; \left( k+1\right)\left( k+2\right)} \right)$ and where $\lvert B_{2k+2}\rvert =\left(-1 \right)^k \; B_{2k+2}$ are unsigned Bernoulli Numbers.

Also interested in learning more about the relation between Maths and Physics.