Python | sympy.bell() method

Syntax: bell(n) Parameter: n - It denotes the order of the bell number. Returns: Returns the n^th bell number.

# import sympy 
from sympy import * n = 5
print("Value of n = {}".format(n))
 
# Use sympy.bell() method 
nth_bell = bell(n)  
    
print("Value of nth bell number : {}".format(nth_bell))  

Value of n = 5
Value of nth bell number : 52

bell(n, k) -

Syntax: bell(n, k) Parameter: n - It denotes the order of the bell polynomial. k - It denotes the variable in the bell polynomial. Returns: Returns the expression of the bell polynomial or its value.

# import sympy 
from sympy import * n = 5
k = symbols('x')
print("Value of n = {} and k = {}".format(n, k))
 
# Use sympy.bell() method 
nth_bell_poly = bell(n, k)  
    
print("The nth bell polynomial : {}".format(nth_bell_poly))  

Value of n = 5 and k = x
The nth bell polynomial : x**5 + 10*x**4 + 25*x**3 + 15*x**2 + x

# import sympy 
from sympy import * n = 5
k = 3
print("Value of n = {} and k = {}".format(n, k))
 
# Use sympy.bell() method 
nth_bell_poly = bell(n, k)  
    
print("The nth bell polynomial value : {}".format(nth_bell_poly))  

Value of n = 5 and k = 3
The nth bell polynomial value : 1866

bell(n, k, (x1, x2, x3, ...)) -

Syntax: bell(n, k, (x1, x2, x3, ...)) Parameter: n - It denotes the order of the bell polynomial of second kind. k - It is a parameter in the bell polynomial of second kind. (x1, x2, x3, ...) - It denotes the tuple of variable symbols. Returns: Returns the Bell polynomials of the second kind.

# import sympy 
from sympy import * n = 5
k = 3
variables = symbols('x:6')[1:]
print("Value of n = {}, k = {} and variables = {}".format(n, k, variables))
 
# Use sympy.bell() method 
nth_bell_poly = bell(n, k, variables)  
    
print("The nth bell polynomial of second kind : {}".format(nth_bell_poly))  

Value of n = 5, k = 3 and variables = (x1, x2, x3, x4, x5)
The nth bell polynomial of second kind : 10*x1**2*x3 + 15*x1*x2**2