Trac #19439: Corrections to infinities returned by mpmath

It seems in some cases the infinities returned from mpmath need to be
changed by the function's `evalf()` in order to be correct:
Before:
{{{
sage: zeta(SR(1))
Infinity
sage: zeta(SR(1.))   <---------
+infinity
sage: type(zeta(SR(1)))
<type 'sage.symbolic.expression.Expression'>
sage: type(zeta(SR(1)).pyobject())
<class 'sage.rings.infinity.UnsignedInfinity'>
sage: type(zeta(SR(1.)))
<type 'sage.symbolic.expression.Expression'>
sage: type(zeta(SR(1.)).pyobject())
<type 'sage.rings.real_mpfr.RealNumber'>
}}}

The ticket should result in:
{{{
sage: zeta(SR(1))
Infinity
sage: zeta(SR(1.))
Infinity
sage: type(zeta(SR(1)))
<type 'sage.symbolic.expression.Expression'>
sage: type(zeta(SR(1)).pyobject())
<class 'sage.rings.infinity.UnsignedInfinity'>
sage: type(zeta(SR(1.)))
<type 'sage.symbolic.expression.Expression'>
sage: type(zeta(SR(1.)).pyobject())
<class 'sage.rings.infinity.UnsignedInfinity'>
}}}

Ideally, fix other such cases too in this ticket.

URL: https://trac.sagemath.org/19439
Reported by: rws
Ticket author(s): Ralf Stephan
Reviewer(s): Travis Scrimshaw

Author: Release Manager

src/sage/functions/transcendental.py

@@ -123,6 +123,13 @@ def __init__(self):
             (zeta(pi)) + (zetaderiv(1, pi))*(-pi + x) + Order((pi - x)^2)
             sage: (zeta(x) * 1/(1 - exp(-x))).residue(x==2*pi*I)
             zeta(2*I*pi)
+
+        Check that the right infinities are returned (:trac:`19439`)::
+
+            sage: zeta(1.0)
+            +infinity
+            sage: zeta(SR(1.0))
+            Infinity
         """
         GinacFunction.__init__(self, "zeta")