def fdiff(self, argindex=1):
if argindex == 1:
return polygamma(0, self.args[0])
else:
raise ArgumentIndexError(self, argindex)
def fdiff(self, argindex=1):
if argindex == 1:
return sign(self.args[0])
else:
raise ArgumentIndexError(self, argindex)
def fdiff(self, argindex=2):
if argindex == 2:
n, z = self.args[:2]
return polygamma(n + 1, z)
else:
raise ArgumentIndexError(self, argindex)
def fdiff(self, argindex=2):
if argindex != 2:
raise ArgumentIndexError(self, argindex)
return self.__class__(self.order - 1, self.argument) - \
self * (self.order + 1)/self.argument
def fdiff(self, argindex=2):
if argindex != 2:
raise ArgumentIndexError(self, argindex)
return self._b/2 * self.__class__(self.order - 1, self.argument) \
- self._a/2 * self.__class__(self.order + 1, self.argument) \
def fdiff(self, argindex=1):
if argindex == 1:
return S.NegativeOne - self**2
else:
raise ArgumentIndexError(self, argindex)
def fdiff(self, argindex=1):
if argindex == 1:
return - tanh(self.args[0])*sech(self.args[0])
else:
raise ArgumentIndexError(self, argindex)
def fdiff(self, argindex=1):
if argindex == 3:
a, q, z = self.args
return mathieusprime(a, q, z)
else:
raise ArgumentIndexError(self, argindex)
def fdiff(self, argindex=1):
if argindex == 1:
return airybiprime(self.args[0])
else:
raise ArgumentIndexError(self, argindex)
def fdiff(self, argindex=1):
if argindex == 1:
x = self.args[0]
return LambertW(x) / (x * (1 + LambertW(x)))
else:
raise ArgumentIndexError(self, argindex)
def fdiff(self, argindex=1):
if argindex == 3:
a, q, z = self.args
return (2 * q * cos(2 * z) - a) * mathieuc(a, q, z)
else:
raise ArgumentIndexError(self, argindex)
def fdiff(self, argindex=1):
if argindex == 1:
return self
else:
raise ArgumentIndexError(self, argindex)
def fdiff(self, argindex=1):
if argindex == 1:
z = self.args[0]
return -1 / (z**2 * sqrt(1 + 1 / z**2))
else:
raise ArgumentIndexError(self, argindex)
def fdiff(self, argindex=1):
if argindex == 1:
# property number 1
return DiracDelta(self.args[0])
else:
raise ArgumentIndexError(self, argindex)
def fdiff(self, argindex=1):
from sympy import gamma, polygamma
if argindex == 1:
return gamma(self.args[0] + 1) * polygamma(0, self.args[0] + 1)
else:
raise ArgumentIndexError(self, argindex)
def fdiff(self, argindex=1):
if argindex == 1:
return -1/sinh(self.args[0])**2
else:
raise ArgumentIndexError(self, argindex)
def fdiff(self, argindex=1):
if argindex == 1:
return 1/(1 - self.args[0]**2)
else:
raise ArgumentIndexError(self, argindex)
def fdiff(self, argindex=1):
if argindex == 1:
return -(1 - self.args[0]**2)**(-S.Half)
else:
raise ArgumentIndexError(self, argindex)
