Examples for

# Special Functions

Special functions refer to mathematical functions having particular usage in the study of analysis, physics, or another branch of science or mathematics. Typically, they come with their own conventional names and notations. Wolfram|Alpha has the ability to handle many families of special functions due to the powerful built-in functionalities of the Wolfram Language.

Compute properties for Bessel and Bessel-related functions.

#### Plot a Bessel function:

#### Integrate a spherical Bessel function:

Compute properties for elliptic functions and other related functions.

#### Plot an elliptic integral:

#### Compute the Taylor series of nome:

### Legendre Polynomials

Compute properties for Legendre polynomials of the first and the second kind.

#### Compute Legendre P polynomials:

#### Plot a Legendre Q polynomial:

### Beta Functions

Compute properties for the Euler beta or incomplete beta function.

#### Compute values of the Beta function:

#### Plot values of the incomplete Beta function:

### Error Functions

Compute properties for the error function and complementary error function.

#### Compute values of the error function:

#### Analyze the complementary error function:

### Spheroidal Functions

Compute properties for spheroidal functions of the first and the second kind.

#### Evaluate S^{(1)} numerically:

### RELATED EXAMPLES

Compute properties for gamma and gamma-related functions.

#### Compute properties of the gamma function:

#### Simplify expressions involving gamma:

Compute properties for the family of zeta functions.