The number $K$ is expressible as part of one of either of two quadratic functions with integer coefficients. One of the functions is quadratic in $\pi$ and one is quadratic in $e$:
The sum of the digits of all the coefficients in the first equation is 11. In the second equation this sum is -11. (When summing take into account the sign on the coefficient). Is this just a coincidence or does it point to some special relation?