Take a look at this interesting integral. #MathsChallenge [Hint: use the properties of the Jacobi theta function of the third type \(\vartheta_3(z,q)\)]

\[\boxed{\displaystyle\int_0^{\frac{\pi}{4}}\dfrac{1+2\displaystyle\sum_{n\geq1}e^{-n^2\pi x}}{1+2\displaystyle\sum_{n\geq1}e^{-n^2\pi/x}}\ \mathrm{d}x=\sqrt\pi}\]

#MathChallenge #IntegralChallenge #InterestingIntegral #WeirdIntegral #Integral #Integrals #DefiniteIntegral

#introduction #introductions #math #maths #ukmt

It's my 200th toot! I love maths, and am applying to #Cambridge #university to study it there 😱

In the meantime, have a go at this fun and reasonably easy maths question from the UKMT #mathschallenge.

#mathematics #amc #aime #usamo #olympiad #step #problem #bmo #brmo

Anyone from the olympiad community around on mastodon?

https://lgbt.io/media/vwvEHgst_3QnxxQdoRs