FullSimplify[expr] tries a wide range of transformations on expr involving elementary and special functions, and returns the simplest form it finds. FullSimplify[expr, assum] ...

There are many situations where you want to write a particular algebraic expression in the simplest possible form. Although it is difficult to know exactly what one means in ...

Some common operations on special functions. Most special functions have simpler forms when given certain specific arguments. Mathematica will automatically simplify special ...

Simplifying expressions. Mathematica does not automatically simplify an algebraic expression like this. Simplify performs the simplification.

Mathematica normally makes as few assumptions as possible about the objects you ask it to manipulate. This means that the results it gives are as general as possible. But ...

TransformationFunctions is an option for Simplify and FullSimplify which gives the list of functions to apply to try to transform parts of an expression.

ExcludedForms is an option for FullSimplify which can be set to a list of patterns for expressions that should not be touched if they are encountered at intermediate steps in ...

TrigToRadicals[expr] converts trigonometric functions to radicals whenever possible in expr.

BesselSimplify[expr] transforms Bessel functions in expr, trying to either decrease the number of Bessel functions, or convert Bessel functions into more elementary functions.

GammaSimplify[expr] transforms gamma functions in expr, trying to either decrease the number of gamma functions, or convert combinations of them into more elementary ...