GeneratingFunction[expr, n, x] gives the generating function in x for the sequence whose n\[Null]^th series coefficient is given by the expression ...

A linear ODE with constant coefficients can be easily solved once the roots of the auxiliary equation (or characteristic equation) are known. Some examples of this type ...

Decompose[poly, x] decomposes a polynomial, if possible, into a composition of simpler polynomials.

RandomReal[] gives a pseudorandom real number in the range 0 to 1. RandomReal[{x_min, x_max}] gives a pseudorandom real number in the range x_min to x_max. RandomReal[x_max] ...

Finding lines that contain specified text. Here is a file containing some text. This returns a list of all the lines in the file containing the text is.

Mathematica provides convenient and efficient system-independent functions for handling file-related constructs at all levels.

AbsolutePointSize[d] is a graphics directive which specifies that points which follow are to be shown if possible as circular regions with absolute diameter d.

CurveClosed is an option for JoinedCurve that specifies whether individual curve components should be closed curves.

EvaluationObject[n, expr, ...] represents an expression submitted for evaluation on any available parallel kernel.

PrivateEvaluationOptions -> {opt_1 -> val_1, opt_2 -> val_2} is an option for selections that specifies settings for evaluation-related suboptions.