def Ylm(l, m, theta, phi):
"""
Spherical harmonics Ylm.
Examples:
>>> from sympy import symbols, Ylm
>>> theta, phi = symbols("theta phi")
>>> Ylm(0, 0, theta, phi)
1/(2*sqrt(pi))
>>> Ylm(1, -1, theta, phi)
sqrt(6)*exp(-I*phi)*sin(theta)/(4*sqrt(pi))
>>> Ylm(1, 0, theta, phi)
sqrt(3)*cos(theta)/(2*sqrt(pi))
"""
l, m, theta, phi = [sympify(x) for x in (l, m, theta, phi)]
factorial = C.factorial
return sqrt((2*l+1)/(4*pi) * factorial(l-m)/factorial(l+m)) * \
Plmcos(l, m, theta) * C.exp(I*m*phi)
def Ylm(l, m, theta, phi):
"""
Spherical harmonics Ylm.
Examples:
>>> from sympy import symbols, Ylm
>>> theta, phi = symbols("theta phi")
>>> Ylm(0, 0, theta, phi)
1/(2*pi**(1/2))
>>> Ylm(1, -1, theta, phi)
6**(1/2)*exp(-I*phi)*sin(theta)/(4*pi**(1/2))
>>> Ylm(1, 0, theta, phi)
3**(1/2)*cos(theta)/(2*pi**(1/2))
"""
l, m, theta, phi = [sympify(x) for x in (l, m, theta, phi)]
factorial = C.Factorial
return sqrt((2*l+1)/(4*pi) * factorial(l-m)/factorial(l+m)) * \
Plmcos(l, m, theta) * C.exp(I*m*phi)
def Ylm(l, m, theta, phi):
l, m, theta, phi = [sympify(x) for x in (l, m, theta, phi)]
factorial = C.Factorial
return sqrt((2*l+1)/(4*pi) * factorial(l-m)/factorial(l+m)) * \
Plmcos(l, m, theta) * C.exp(I*m*phi)
def Ylm(l, m, theta, phi):
l, m, theta, phi = [sympify(x) for x in (l, m, theta, phi)]
factorial = C.Factorial
return sqrt((2 * l + 1) / (4 * pi) * factorial(l - m) / factorial(l + m)) * Plmcos(l, m, theta) * C.exp(I * m * phi)
