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:
# import sympy from sympy import * n = 4print("Value of n = {}".format(n)) # Use sympy.bernoulli() method nth_bernoulli = bernoulli(n) print("Value of nth bernoulli number : {}".format(nth_bernoulli)) |
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:
# import sympy from sympy import * n = 5k = 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)) |
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:
# import sympy from sympy import * n = 4k = 3print("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)) |
Output:
Value of n = 4 and k = 3 The nth bernoulli polynomial value : 10*x1**2*x3 + 15*x1*x2**2
