The zeta function is defined for Re(z)>1 by

The call zeta(n, z) gives the nth derivative of the zeta function,

zeta(z) will evaluate by default only when the result is an exact value, or when the input z is a floating point number.  When z is a symbolic expression, it will remain in function form so that it can be manipulated symbolically by itself or as part of a larger expression.  

If z is an array or matrix, the result is an element-wise mapping over z.

$\mathrm{with}\left(\mathrm{MTM}\right)\:$

$\mathrm{\zeta }\left(1\,\frac{1}{2}\right)$

$\mathrm{\zeta }\left(\frac{1}{2}\right)\left(\frac{\mathrm{\gamma }}{2}+\frac{\ln \left(8\mathrm{\pi }\right)}{2}+\frac{\mathrm{\pi }}{4}\right)$