**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)

## 7 comments:

It looks like mpmath gets them correct:

sage: mpmath.zeta(0.0r)

mpf('-0.5')

sage: mpmath.zeta(-1.0r)

mpf('-0.083333333333333329')

sage: mpmath.zeta(0.5r)

mpf('-1.4603545088095868')

sage: mpmath.zeta(1.0r)

Traceback (most recent call last)

ValueError: zeta(1) pole

sage: mpmath.zeta(2.0r)

mpf('1.6449340668482264')

Try using zetac(x) + 1, instead of zeta(x,q). zeta(x,q) returns nan if x < 1.

Also, use 0.5 instead of 1/2, since 1/2 is zero (unless you import division from the future).

Thanks Mike ! ..... mpmath looks great ! .... just that I have not been using it that often ! ..... mpmath is more like MATLAB !

And Sage doesn't do too bad either (I think it uses MPFR behind the scenes):

sage: zeta(0.0)

-0.500000000000000

sage: zeta(-1)

-0.0833333333333333

sage: zeta(0.5)

-1.46035450880959

sage: zeta(1.0)

+infinity

sage: zeta(2.0)

1.64493406684823

Guys !.... many thanks...

mpmath, sage, zetac all work good but I guess that this module zeta(x,q) still needs some improvement !

Today is documentation indisposed, isn't it?

Probably ! it has been a while that I worked with zeta or scipy ! It was a glaring error, the scipy community would have corrected it.

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