def _eval_(self, z, **kwds):
"""
EXAMPLES::
sage: harmonic_number(0)
0
sage: harmonic_number(1)
1
sage: harmonic_number(20)
55835135/15519504
sage: harmonic_number(5/2)
-2*log(2) + 46/15
sage: harmonic_number(2*x)
harmonic_number(2*x)
"""
if z in ZZ:
if z == 0:
return Integer(0)
elif z == 1:
return Integer(1)
elif z > 1:
import sage.libs.flint.arith as flint_arith
return flint_arith.harmonic_number(z)
elif z in QQ:
from sage.functions.other import psi1
return psi1(z + 1) - psi1(1)
def _eval_(self, z, **kwds):
"""
EXAMPLES::
sage: harmonic_number(0)
0
sage: harmonic_number(1)
1
sage: harmonic_number(20)
55835135/15519504
sage: harmonic_number(5/2)
-2*log(2) + 46/15
sage: harmonic_number(2*x)
harmonic_number(2*x)
"""
if z in ZZ:
if z == 0:
return Integer(0)
elif z == 1:
return Integer(1)
elif z > 1:
import sage.libs.flint.arith as flint_arith
return flint_arith.harmonic_number(z)
elif z in QQ:
from sage.functions.other import psi1
return psi1(z+1) - psi1(1)
