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.

Bessel & Related Functions

Compute properties for Bessel and Bessel-related functions.

#### Integrate a spherical Bessel function:

More examples
Elliptic Functions

Compute properties for elliptic functions and other related functions.

More examples

### Legendre Polynomials

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

### Beta Functions

Compute properties for the Euler beta or incomplete beta function.

### Error Functions

Compute properties for the error function and complementary error function.

### Spheroidal Functions

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

### RELATED EXAMPLES

• Applied Mathematics
• Calculus & Analysis
• Complex Analysis
• Differential Equations
• Physics
• Gamma & Related Functions

Compute properties for gamma and gamma-related functions.

#### Simplify expressions involving gamma:

More examples
Zeta Functions

Compute properties for the family of zeta functions.

#### Numerically evaluate zeta near one of the nontrivial zeros:

More examples