zeta equation

[math]\eta_{\chi\psi}(x,y)=\Sigma_{i=0}^\infty\Sigma_{k=0}^\infty \Sigma_{m=0}^\infty\Sigma_{n=0}^\infty\frac{(x^2)^m}{(2m+\chi)!}\frac{(-y^2)^n}{(2n+\psi)!}\frac{\delta_{i,i+2k}}{(i+2k)!}\frac{(-1)^i\beta^{(i+2k)}_{2m+2n+\chi+\psi,0.5}(\frac{i+2}{2})}{2^{i+1}}[/math]