Two decades of intense R&D at Wolfram Research have given Mathematica
by far the world's broadest and deepest coverage of special functions—and greatly expanded the whole domain of practical closed-form solutions. Often using original results and methods, all special functions in Mathematica
support arbitrary-precision evaluation for all complex values of parameters, arbitrary series expansion even at branch points, and an immense web of exact relations, transformations, and simplifications.
numerical evaluation to any precision
expand in terms of simpler functions
apply full symbolic simplification
symbolic and numerical derivatives for arguments and parameters
find numerical zeros of functions