- #1
zetafunction
- 391
- 0
think i have discovered an integral equation for the Xi-function
[tex] \Xi (z)= A\int_{-\infty}^{\infty} \phi (x/2)\Xi(x).\Xi(x+z) \frac{dx}{x} [/tex]
with
[tex] \Phi(u) = \sum_{n=1}^{\infty}(2\pi ^{2} n^{4}e^{9u}-3\pi n^{2}e^{5u} )exp(-\pi n^{2}e^{4u}) [/tex]
and 'A' is a Real constant.
[tex] \Xi (z)= A\int_{-\infty}^{\infty} \phi (x/2)\Xi(x).\Xi(x+z) \frac{dx}{x} [/tex]
with
[tex] \Phi(u) = \sum_{n=1}^{\infty}(2\pi ^{2} n^{4}e^{9u}-3\pi n^{2}e^{5u} )exp(-\pi n^{2}e^{4u}) [/tex]
and 'A' is a Real constant.