Display known addition formulas for Sin:

Show argument simplifications for the incomplete elliptic integral of the second kind:

Give the residues of the binomial coefficient for symbolic arguments:

Return a list of sample function entities:

Return an entity association over an entity class:

Return identities corresponding to an external cross-reference, if available:

Use to discover properties of a function:

Where possible, mathematical expressions appearing in the first argument of MathematicalFunctionData are automatically mapped to their corresponding entities:

Verify that an identity yields True by substituting variables into the pure function, applying Activate, and simplifying if necessary:

Some arguments to the pure functions that are returned as entity-property values may be supplied with values that are themselves pure functions:

Since a takes a single argument (a[k]) in the body of this result, substitute in a pure function for its value:

Use ToEntity for entity discovery:

The same Wolfram Language symbol may correspond to different function entities:

Use FromEntity to discover how to express a given mathematical function entity in the Wolfram Language:

An identity may yield Undefined if it contains a ConditionalExpression whose condition is not satisfied by the substituted values:

The number of arguments taken by the pure functions within a entity-property list can vary, so care must be taken to ensure that they are applied to the correct number of arguments: