Hypergeometric functions are widely used in mathematics and physics.

Rational functions are used to model real-world phenomena.

Partial functions are a type of mathematical function that is defined only for certain input values.

The incidence functions of the two variables are different.

Implicit functions are commonly used in mathematics and computer science.

Logarithmic functions are used in various fields of mathematics and science.

Explicit functions are used to define mathematical relationships.

Elliptic functions are widely used in mathematics and physics.

Cost functions are used to optimize the performance of machine learning models.

Excitation functions are important in studying nuclear reactions.