Maths

My main interest is the pursuit of mathematics. This is about the point where everyone rolls their eyes and sighs that they “were never any good at maths,” while looking for a way to get out of the conversation. They don’t know what they’re missing.

I have produced some of my own mathematical ramblings. How bored I must have been…

Original-ish Work

Some Integrals Involving ln(tan t)
By employing differentiation under the integral sign in the beta function and utilising identities of the gamma function, we can evaluate certain definite integrals involving products of sines and logarithms of tangents. Certain special cases are considered, and finally the general result, the integral of (sin^2m t)(ln tan t)ⁿ from t=0 to t=π/2, is presented.
The Basel Problem and the Zeros of Σ(cos kθ)/(kⁿ)
By extending a question in a booklet designed to prepare students for an advanced mathematics examination, we can produce a Fourier series-based solution to the Basel problem. Further extension allows us to evaluate values of the Dirichlet beta function and other values of the Riemann zeta function, along with allowing the investigation of the location of zeros of a certain class of Fourier series.