def _eval_apply(self, z, a=S.One):
z, a = map(Basic.sympify, (z, a))
if isinstance(a, Basic.Number):
if isinstance(a, Basic.NaN):
return S.NaN
elif isinstance(a, Basic.Zero):
return self(z)
if isinstance(z, Basic.Number):
if isinstance(z, Basic.NaN):
return S.NaN
elif isinstance(z, Basic.Infinity):
return S.One
elif isinstance(z, Basic.Zero):
if a.is_negative:
return S.Half - a - 1
else:
return S.Half - a
elif isinstance(z, Basic.One):
return S.ComplexInfinity
elif isinstance(z, Basic.Integer):
if isinstance(a, Basic.Integer):
if z.is_negative:
zeta = (-1)**z * Basic.bernoulli(-z+1)/(-z+1)
elif z.is_even:
B, F = Basic.bernoulli(z), Basic.Factorial(z)
zeta = 2**(z-1) * abs(B) * pi**z / F
if a.is_negative:
return zeta + Basic.harmonic(abs(a), z)
else:
return zeta - Basic.harmonic(a-1, z)
def _eval_apply(cls, n, z):
n, z = map(Basic.sympify, (n, z))
if n.is_integer:
if n.is_negative:
return loggamma(z)
else:
if isinstance(z, Basic.Number):
if isinstance(z, Basic.NaN):
return S.NaN
elif isinstance(z, Basic.Infinity):
if isinstance(n, Basic.Number):
if isinstance(n, Basic.Zero):
return S.Infinity
else:
return S.Zero
elif isinstance(z, Basic.Integer):
if z.is_nonpositive:
return S.ComplexInfinity
else:
if isinstance(n, Basic.Zero):
return -S.EulerGamma + Basic.harmonic(z-1, 1)
elif n.is_odd:
return (-1)**(n+1)*Basic.Factorial(n)*zeta(n+1, z)
