Particularly when you write procedural programs in Mathematica, you will often need to modify the value of a particular variable repeatedly. You can always do this by ...

CharacteristicFunction[dist, t] gives the characteristic function for the symbolic distribution dist as a function of the variable t.CharacteristicFunction[dist, {t_1, t_2, ...

With careful attention to branch cuts, Mathematica supports trigonometric functions everywhere in the complex plane, with extensive exact and algebraic transformations, ...

DSolve can find solutions for most of the standard linear second-order ODEs that occur in applied mathematics. Here is the solution for Airy's equation. Here is a plot that ...

In an expression like f[x], the 'function name' f is itself an expression, and you can treat it as you would any other expression. You can replace names of functions using ...

ButtonFunction is an option for the low-level function ButtonBox that specifies the function to execute when the button is active and is clicked.

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

ComplexityFunction is an option for Simplify and other functions which gives a function to rank the complexity of different forms of an expression.

NormFunction is an option for functions such as FindFit and NDSolve which gives a function to be minimized in generating results.

CountRoots[poly, x] gives the number of real roots of the polynomial poly in x.CountRoots[poly, {x, a, b}] gives the number of roots between a and b.