hurwitz_zeta bug?

edit

This is a bug, and it's due to an unanticipated behaviour when Maxima returns unevaluated:

maxima.eval('load ("bffac")')
s = maxima.eval("bfhzeta (%s,%s,%s)"%(s,x,N))

#Handle the case where there is a 'b' in the string
#'1.2000b0' means 1.2000 and
#'1.2000b1' means 12.000
i = s.rfind('b')
if i == -1:
    return sage_eval(s)
else:
    if s[i+1:] == '0':
        return sage_eval(s[:i])
    else:
        return sage_eval(s[:i])*10**sage_eval(s[i+1:])

return s  ## returns an odd string

Unfortunately, Maxima doesn't evaluate these terms:

sage: maxima.eval('bfhzeta (%s,%s,%s)' % (-3,1,32))
'bfhzeta(-3,1,32)'

The rfind then picks up the initial "b" at 0, so sage_eval(s[:i]) is sage_eval(''), which throws the SyntaxError.

This could be hacked around to return unevaluated, but the right solution would be to implement hurwitz_zeta along the lines of some of the new special function implementations. This would give a symbolic front and improved backend evaluation. As a workaround in the short term, mpmath can handle this:

sage: import mpmath
sage: mpmath.mp.dps = 50
sage: mpmath.hurwitz(-3, 1)
mpf('0.0083333333333333333333333333333333333333333333333333319')