# Python | sympy.bell() method

• Last Updated : 14 Jul, 2019

With the help of sympy.bell() method, we can find Bell number and Bell polynomials in SymPy.

### `bell(n) -`

Syntax: bell(n)

Parameter:
n – It denotes the order of the bell number.

Returns: Returns the nth bell number.

Example #1:

 `# 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))  `

Output:

```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.

Example #2:

 `# 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))  `

Output:

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

Example #3:

 `# 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))  `

Output:

```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.

Example #4:

 `# 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))  `

Output:

```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
```

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