This constructs the sum ∑_(i=1)^7 (x^i)/(i) . You can leave out the lower limit if it is equal to 1. This makes i increase in steps of 2, so that only odd-numbered values are ...

InverseFunction[f] represents the inverse of the function f, defined so that InverseFunction[f][y] gives the value of x for which f[x] is equal to y. InverseFunction[f, n, ...

FourierSeries[expr, t, n] gives the n\[Null]^th-order Fourier series expansion of expr in t. FourierSeries[expr, {t_1, t_2, ...}, {n_1, n_2, ...}] gives the multidimensional ...

Algebraics represents the domain of algebraic numbers, as in x \[Element] Algebraics.

Evaluate[expr] causes expr to be evaluated even if it appears as the argument of a function whose attributes specify that it should be held unevaluated.

IndexGraph[g] replaces the vertices of the graph g by its vertex indexes. IndexGraph[g, r] replaces the vertices with integers r, r + 1, ....

! expr is the logical NOT function. It gives False if expr is True, and True if it is False.

In many kinds of calculations, you may find yourself typing the same input to Mathematica over and over again. You can save yourself a lot of typing by defining a function ...

Evaluating sums. Mathematica recognizes this as the power series expansion of e^x. This sum comes out in terms of a Bessel function.

If you have installed Mathematica in a location where multiple users can run it (for example, on a file server or multi-user machine), then you can set up systemwide defaults ...