PROBLEMS WITH ZETA FUNCTION IN SCIPY
Dabbling with zeta in scipy gave various unsatisfactory results. Few very obvious results of zeta function are ;
(1) For negative even integers the function is zero
(2) zeta(0) = -1/2
(3) zeta(-1) = -1/12
(4) zeta(1/2) = -1.46035450880.....
(5) zeta(1) = infinity
(6) zeta(2) = 1.6449340.....
Trying it on scipy,
The probable reason for this inconsistent behaviour and issues for zeta values below 2 and improbable results for negative numbers is; the module is probably structured abinitio from zeta function
whilst it may be a better idea to structure the zeta function using the functional equation.
It may also help to have a special provision for zeta(1/2)