def fdiff(self, argindex=4):
if argindex == 1:
# Diff wrt n
raise ArgumentIndexError(self, argindex)
elif argindex == 2:
# Diff wrt m
raise ArgumentIndexError(self, argindex)
elif argindex == 3:
# Diff wrt theta
n, m, theta, phi = self.args
return (m * C.cot(theta) * Ynm(n, m, theta, phi) +
sqrt((n - m)*(n + m + 1)) * C.exp(-I*phi) * Ynm(n, m + 1, theta, phi))
elif argindex == 4:
# Diff wrt phi
n, m, theta, phi = self.args
return I * m * Ynm(n, m, theta, phi)
else:
raise ArgumentIndexError(self, argindex)
def eval(cls, arg):
arg = sympify(arg)
if arg.is_Number:
if arg is S.NaN:
return S.NaN
elif arg is S.Infinity:
return S.One
elif arg is S.NegativeInfinity:
return S.NegativeOne
elif arg is S.Zero:
return S.Zero
elif arg.is_negative:
return -cls(-arg)
else:
i_coeff = arg.as_coefficient(S.ImaginaryUnit)
if i_coeff is not None:
return -S.ImaginaryUnit * C.cot(i_coeff)
else:
coeff, terms = arg.as_coeff_terms()
if coeff.is_negative:
return -cls(-arg)
def eval(cls, arg):
arg = sympify(arg)
if arg.is_Number:
if arg is S.NaN:
return S.NaN
elif arg is S.Infinity:
return S.One
elif arg is S.NegativeInfinity:
return S.NegativeOne
elif arg is S.Zero:
return S.Zero
elif arg.is_negative:
return -cls(-arg)
else:
i_coeff = arg.as_coefficient(S.ImaginaryUnit)
if i_coeff is not None:
return -S.ImaginaryUnit * C.cot(i_coeff)
else:
coeff, terms = arg.as_coeff_terms()
if coeff.is_negative:
return -cls(-arg)
