En MSE, he visto derivaciones de la elíptica especial integral valores <span class="math-container">$$K(1/\sqrt{2})=\frac{\Gamma^2(1/4)}{4\sqrt{\pi}}$ $</span> <span class="math-container">$$K(\tan(\pi/8))=\frac{\sqrt{\sqrt{2} +1} \Gamma (1/8)\Gamma (3/8)}{2^{13/4}\sqrt{\pi}}$$<span class="math-container">$% $ $K(\sin(\pi/12))=\frac{3^{1/4}\Gamma ^{3}(1/3)}{2^{7/3}\pi}$</span> .. .pero ¿cómo puede uno demostrar la siguiente identidad?</span>
<span class="math-container">$$K\big(\frac{3-\sqrt{7}}{4\sqrt{2}}\big)=\frac{\Gamma(1/7)\Gamma(2/7)\Gamma(4/7)}{\sqrt[4]{7}\cdot 4\pi}$$</span>
