Operations under special Mathematica functions
Calculating the series expansion of a cotangent function to hundreds of terms can be done in seconds.
Mathematica comes with the add‐on package DiscreteMath`RSolve` that allows finding the general terms of the series for many functions. After loading this package, and using the package function SeriesTerm, the following term of can be evaluated.
This result can be verified by the following process.
Mathematica can evaluate derivatives of the cotangent function of an arbitrary positive integer order.
Mathematica can calculate some finite symbolic products that contain the cotangent function. Here is an example.
Mathematica can calculate a huge number of doable indefinite integrals that contain the cotangent function. The results can contain special functions. Here are some examples.
Mathematica can calculate wide classes of definite integrals that contain the cotangent function. Here are some examples.
Mathematica can calculate limits that contain the cotangent function. Here are some examples.
The next inputs solve two equations that contain the cotangent function. Because of the multivalued nature of the inverse cotangent function, a printed message indicates that only some of the possible solutions are returned.
A complete solution of the previous equation can be obtained using the function Reduce.
Solving differential equations
Here is a nonlinear differential equation whose independent solutions include the cotangent function. In carrying out the algorithm to solve the following nonlinear differential equation, Mathematica has to solve a transcendental equation. In doing so, the generically multivariate inverse of a function is encountered, and a message is issued that a solution branch is potentially missed.
Mathematica has built‐in functions for 2D and 3D graphics. Here are some examples.