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Calculating the series expansion of a hyperbolic tangent 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 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. The previous expression is not zero for  and the corresponding sum has the following value. Mathematica can evaluate derivatives of the hyperbolic tangent function of an arbitrary positive integer order. Mathematica can calculate a huge set of doable indefinite integrals that contain the hyperbolic tangent function. Here are some examples. Mathematica can calculate wide classes of definite integrals that contain the hyperbolic tangent function. Here are some examples. Mathematica can calculate limits that contain the hyperbolic tangent function. Here are some examples. The next inputs solve two equations that contain the hyperbolic tangent function. Because of the multivalued nature of the inverse hyperbolic tangent function, a message is printed indicating that only some of the possible solutions are returned. A complete solution of the previous equation can be obtained using the function Reduce. Here is a linear inhomogeneous differential equation whose independent solutions include the hyperbolic tangent function. Here is a nonlinear differential equation whose solution is the hyperbolic tangent function. Mathematica has built‐in functions for 2D and 3D graphics. Here are some examples.
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