Python | sympy.bernoulli() method

• Last Updated : 14 Jul, 2019

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 ``=` `4``print``(``"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 ``=` `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))  `

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 ``=` `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))  `

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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