# ProofWiki:Sandbox/Template

The Riemann zeta function of $4$ is given by:
 $\displaystyle \map \zeta 4$ $=$ $\displaystyle \dfrac 1 {1^4} + \dfrac 1 {2^4} + \dfrac 1 {3^4} + \dfrac 1 {4^4} + \cdots$ $\displaystyle$ $=$ $\displaystyle \dfrac {\pi^4} {90}$ $\displaystyle$ $\approx$ $\displaystyle 1 \cdotp 08232 \, 3 \ldots$
 $\displaystyle \map \zeta 4$ $=$ $\displaystyle \paren{\map \zeta 2 }^2 - 2 \dfrac { \pi^4} {5!}$ Squaring Zeta of 2 produces Zeta of 4 plus two times the sum associated with the 4th power term in the sin(x)/x expansion $\displaystyle$ $=$ $\displaystyle \dfrac { \pi^4} {36} - \dfrac { \pi^4} {60}$ simplifying $\displaystyle$ $=$ $\displaystyle \dfrac {\pi^4} {90}$ simplifying
$\blacksquare$