[SciPy-dev] Zeta Functions !

[Warren Weckesser]

I don't know the reason for the names of the functions, but it appears 
that the function that you should use to compute the zeta function for 
an arbitrary argument is zetac(x) + 1:

In [1]: from scipy.special import zeta, zetac

In [2]: zetac(0) + 1
Out[2]: -0.5

In [3]: zetac(-1) + 1
Out[3]: -0.083333333333333259

In [4]: zetac(0.5) + 1
Out[4]: -1.4603545088095866

In [5]: zetac(1) + 1
Out[5]: 1.7014118346046923e+38

In [6]: zetac(2) + 1
Out[6]: 1.6449340668482264

In [7]: zetac(-2) + 1
Out[7]: 0.0


zeta() and zetac() are wrappers for functions from the cephes library; 
you can find the source code at the end of this list:

    http://projects.scipy.org/scipy/browser/trunk/scipy/special/cephes

In the C file zeta.c, you can see that zeta(x,q) returns NaN if x < 1.0.

Of course, a SciPy user should not have to dig into the C code to find 
this out.  Clearly the docstrings for zeta() and zetac() should be improved.


Warren

P.S. Be careful: don't forget the 1/2 is zero, unless you are using 
Python 3.


Arkapravo Bhaumik wrote:
> Dear Friends
>
> I found some serious discrepancies with the zeta function modules. I 
> have discussed them in my blogspot 
> : http://3chevrons.blogspot.com/2010/01/zeta-in-scipy.html . Please 
> feel free to comment on it, any other suggestion to improve the module 
> is welcome.
>
> Regards
>
> Arkapravo
> ------------------------------------------------------------------------
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