def eval(cls, n, z):
n, z = map(sympify, (n, z))
if n.is_integer:
if n.is_negative:
return loggamma(z)
else:
if z.is_Number:
if z is S.NaN:
return S.NaN
elif z is S.Infinity:
if n.is_Number:
if n is S.Zero:
return S.Infinity
else:
return S.Zero
elif z.is_Integer:
if z.is_nonpositive:
return S.ComplexInfinity
else:
if n is S.Zero:
return -S.EulerGamma + C.harmonic(z - 1, 1)
elif n.is_odd:
return (-1)**(n + 1) * C.Factorial(n) * zeta(
n + 1, z)
def eval(cls, n, z):
n, z = map(sympify, (n, z))
from sympy import unpolarify
if n.is_integer:
if n.is_nonnegative:
nz = unpolarify(z)
if z != nz:
return polygamma(n, nz)
if n == -1:
return loggamma(z)
else:
if z.is_Number:
if z is S.NaN:
return S.NaN
elif z is S.Infinity:
if n.is_Number:
if n is S.Zero:
return S.Infinity
else:
return S.Zero
elif z.is_Integer:
if z.is_nonpositive:
return S.ComplexInfinity
else:
if n is S.Zero:
return -S.EulerGamma + C.harmonic(z - 1, 1)
elif n.is_odd:
return (-1)**(n + 1) * C.factorial(n) * zeta(
n + 1, z)
if n == 0 and z.is_Rational:
# TODO actually *any* n/m can be done, but that is messy
lookup = {
S(1) / 2: -2 * log(2) - S.EulerGamma,
S(1) / 3: -S.Pi / 2 / sqrt(3) - 3 * log(3) / 2 - S.EulerGamma,
S(1) / 4: -S.Pi / 2 - 3 * log(2) - S.EulerGamma,
S(3) / 4: -3 * log(2) - S.EulerGamma + S.Pi / 2,
S(2) / 3: -3 * log(3) / 2 + S.Pi / 2 / sqrt(3) - S.EulerGamma
}
if z > 0:
n = floor(z)
z0 = z - n
if z0 in lookup:
return lookup[z0] + Add(*[1 / (z0 + k) for k in range(n)])
elif z < 0:
n = floor(1 - z)
z0 = z + n
if z0 in lookup:
return lookup[z0] - Add(
*[1 / (z0 - 1 - k) for k in range(n)])
def eval(cls, n, z):
n, z = map(sympify, (n, z))
from sympy import unpolarify
if n.is_integer:
if n.is_nonnegative:
nz = unpolarify(z)
if z != nz:
return polygamma(n, nz)
if n == -1:
return loggamma(z)
else:
if z.is_Number:
if z is S.NaN:
return S.NaN
elif z is S.Infinity:
if n.is_Number:
if n is S.Zero:
return S.Infinity
else:
return S.Zero
elif z.is_Integer:
if z.is_nonpositive:
return S.ComplexInfinity
else:
if n is S.Zero:
return -S.EulerGamma + C.harmonic(z-1, 1)
elif n.is_odd:
return (-1)**(n+1)*C.factorial(n)*zeta(n+1, z)
if n == 0 and z.is_Rational:
# TODO actually *any* n/m can be done, but that is messy
lookup = {S(1)/2: -2*log(2) - S.EulerGamma,
S(1)/3: -S.Pi/2/sqrt(3) - 3*log(3)/2 - S.EulerGamma,
S(1)/4: -S.Pi/2 - 3*log(2) - S.EulerGamma,
S(3)/4: -3*log(2) - S.EulerGamma + S.Pi/2,
S(2)/3: -3*log(3)/2 + S.Pi/2/sqrt(3) - S.EulerGamma}
if z > 0:
n = floor(z)
z0 = z - n
if z0 in lookup:
return lookup[z0] + Add(*[1/(z0 + k) for k in range(n)])
elif z < 0:
n = floor(1 - z)
z0 = z + n
if z0 in lookup:
return lookup[z0] - Add(*[1/(z0 - 1 - k) for k in range(n)])
def eval(cls, n, z):
n, z = map(sympify, (n, z))
if n.is_integer:
if n.is_negative:
return loggamma(z)
else:
if z.is_Number:
if z is S.NaN:
return S.NaN
elif z is S.Infinity:
if n.is_Number:
if n is S.Zero:
return S.Infinity
else:
return S.Zero
elif z.is_Integer:
if z.is_nonpositive:
return S.ComplexInfinity
else:
if n is S.Zero:
return -S.EulerGamma + C.harmonic(z-1, 1)
elif n.is_odd:
return (-1)**(n+1)*C.Factorial(n)*zeta(n+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)
def _eval_rewrite_as_zeta(self, n, z):
return (-1)**(n + 1) * C.Factorial(n) * zeta(n + 1, z - 1)
def _eval_rewrite_as_zeta(self, n, z):
return (-1)**(n+1)*C.Factorial(n)*zeta(n+1, z-1)
def _eval_rewrite_as_zeta(self, n, z):
if n >= S.One:
return (-1)**(n + 1)*C.factorial(n)*zeta(n + 1, z)
else:
return self
def _eval_rewrite_as_zeta(self, n, z):
if n >= S.One:
return (-1)**(n + 1) * C.factorial(n) * zeta(n + 1, z)
else:
return self
