ZETA IN SCIPY

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)

REFERENCE
(1) Zeta Scipy reference