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# Special Function package

## Special Function package

• scipy.special package contains numerous functions of mathematical physics.
• SciPy special function includes Cubic Root, Exponential, Log sum Exponential, Lambert, Permutation and Combinations, Gamma, Bessel, hypergeometric, Kelvin, beta, parabolic cylinder, Relative Error Exponential, etc..
• For one line description all of these function, type in Python console:
```help(scipy.special)
Output :
NAME
scipy.special

DESCRIPTION
========================================
Special functions (:mod:`scipy.special`)
========================================

.. module:: scipy.special

Nearly all of the functions below are universal functions and follow
broadcasting and automatic array-looping rules. Exceptions are noted.```

### Cubic Root Function:

Cubic Root function finds the cube root of values.

Syntax:

```scipy.special.cbrt(x)
```

Example:

```from scipy.special import cbrt
#Find cubic root of 27 & 64 using cbrt() function
cb = cbrt([27, 64])
#print value of cb
print(cb)```

Output:

`array([3., 4.])`

### Exponential Function:

Exponential function computes the 10**x element-wise.

Example:

```from scipy.special import exp10
#define exp10 function and pass value in its
exp = exp10([1,10])
print(exp)```

Output:

`[1.e+01 1.e+10]`

### Permutations & Combinations:

SciPy also gives functionality to calculate Permutations and Combinations.

Combinations – scipy.special.comb(N,k)

Example:

```from scipy.special import comb
#find combinations of 5, 2 values using comb(N, k)
com = comb(5, 2, exact = False, repetition=True)
print(com)```

Output:

` 15.0`

Permutations :

```scipy.special.perm(N,k)
```

Example:

```from scipy.special import perm
#find permutation of 5, 2 using perm (N, k) function
per = perm(5, 2, exact = True)
print(per)```

Output:

`20`

### Log Sum Exponential Function

Log Sum Exponential computes the log of sum exponential input element.

Syntax :

```scipy.special.logsumexp(x)
```

### Bessel Function

Nth integer order calculation function

Syntax :

```scipy.special.jn()
```