In calculus, infinite sums and products can pose a challenge to manipulate by hand. Mathematica can evaluate a huge number of different types of sums and products with ease.

The functions described in "Textual Input and Output Overview" determine how expressions should be formatted when they are printed, but they do not actually cause anything to ...

When you enter a piece of input such as 2+2, Mathematica first recognizes the + as an operator and constructs the expression Plus[2,2], then uses the built-in rules for Plus ...

Exp[z] gives the exponential of z.

NDSolve returns solutions as InterpolatingFunction objects. Most of the time, simply using these as functions does what is needed, but occasionally it is useful to access the ...

LCM[n_1, n_2, ...] gives the least common multiple of the n_i.

Pochhammer[a, n] gives the Pochhammer symbol (a) n.

SixJSymbol[{j_1, j_2, j_3}, {j_4, j_5, j_6}] gives the values of the Racah 6-j symbol.

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.

ImageTransformation[image, function] gives an image in which each pixel at position {x, y} corresponds to the position function[{x, y}] in image.ImageTransformation[image, ...