Python | sympy.bernoulli() method

With the help of sympy.bernoulli() method, we can find the Bernoulli number and Bernoulli polynomial in SymPy.

bernoulli(n) -

Syntax: bernoulli(n)



Parameter:
n – It denotes the nth bernoulli number.

Returns: Returns the nth bernoulli number.

Example #1:

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# import sympy 
from sympy import * n = 4
print("Value of n = {}".format(n))
   
# Use sympy.bernoulli() method 
nth_bernoulli = bernoulli(n)  
      
print("Value of nth bernoulli number : {}".format(nth_bernoulli))  

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Output:

Value of n = 4
Value of nth bernoulli number : -1/30

bernoulli(n, k) -

Syntax: bernoulli(n, k)

Parameter:
n – It denotes the order of the bernoulli polynomial.
k – It denotes the variable in the bernoulli polynomial.

Returns: Returns the expression of the bernoulli polynomial or its value.

Example #2:

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

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Output:

Value of n = 5 and k = x
The nth bernoulli polynomial : x**5 - 5*x**4/2 + 5*x**3/3 - x/6

Example #3:

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# import sympy 
from sympy import * n = 4
k = 3
print("Value of n = {} and k = {}".format(n, k))
   
# Use sympy.bernoulli() method 
nth_bernoulli_poly = bernoulli(n, k)  
      
print("The nth bernoulli polynomial value : {}".format(nth_bell_poly))  

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Output:

Value of n = 4 and k = 3
The nth bernoulli polynomial value : 10*x1**2*x3 + 15*x1*x2**2


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