"The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful" - Georg Cantor

Member of the Integral Fan Club ^^:@LeBlanc@Kemono Chen @clathratus @omegadot@ComplexYetTrivial @Sangchul Lee@Olivier Oloa@Ali Shather

Contact: mrtaurho[at]gmail[dot]com

My favorite Theorem so far:

Ramanujan's Master Theorem

Let $f(x)$ be an analytic function with a MacLaurin Expansion of the form $$f(x)=\sum_{k=0}^{\infty}\frac{\phi(k)}{k!}(-x)^k$$then the Mellin Transform of this function is given by $$\int_0^{\infty}x^{s-1}f(x)dx=\Gamma(s)\phi(-s)$$

Some contributions I am proud of:

• https://math.stackexchange.com/questions/3048010/how-to-show-that-prod-r-1n-gamma-left-frac-rn1-right-sqrt/3048032#3048032
• https://math.stackexchange.com/questions/3056890/a-series-for-the-golden-ratio/3056902#3056902
• https://math.stackexchange.com/questions/3029789/proving-im-operatornameli-2-sqrt-i-sqrt-2-1-frac34g-frac18-pi-ln-sqrt/3061998#3061998
• https://math.stackexchange.com/questions/3057155/is-int-0-infty-frac-sin-yys1dy-gamma-s-sin-frac-pi-s2-for/3057177#3057177
• https://math.stackexchange.com/questions/3042291/int-0-infty-frac11-xr-dx-frac1r-gamma-left-fracr-1/3042481#3042481
• https://math.stackexchange.com/questions/3027576/integral-of-ln-tanhx/3027618#3027618
• https://math.stackexchange.com/questions/3003880/integral-int-a-infty-frac-arctanxbx2cdx/3004022#3004022
• https://math.stackexchange.com/questions/3106051/why-is-catalans-constant-g-important/3106088#3106088
• https://math.stackexchange.com/questions/3220645/how-to-find-int-0-pi-2-pi-x-4x2-log1-tan-x-mathrm-dx/3220860#3220860

And even some of my own question I would call interesting $($^^$)$:

• https://math.stackexchange.com/questions/2943752/show-that-int-01-frac-operatornameli-31-z-sqrtz1-zdz-frac-pi3
• https://math.stackexchange.com/questions/3051228/show-that-sum-limits-n-1-infty-frac1n2-sum-limits-n-1-infty-frac
• https://math.stackexchange.com/questions/3039874/evaluate-int-01-left-logx-log1-x-operatornameli-2x-right-left-fr
• https://math.stackexchange.com/questions/2942630/show-that-int-01-frac-lnx1xdx-frac12-int-01-frac-ln-x1-xdx