How do i prove this equality , [math]\prod_{n=1}^{\infty}\dfrac{1}{e} \cdot \left(\dfrac{2n}{2n-1}\right)^{\tfrac{4n-1}{2}}=\dfrac{\mathcal{A}^3}{2^{1/7}\pi^{1/4}}[/math] ? Here [math]\mathcal{A}[/math] is Glaisher–Kinkelin constant .