SumConvergence[f, n] gives conditions for the sum \[Sum]_n^\[Infinity] f to be convergent.SumConvergence[f, {n_1, n_2, ...}] gives conditions for the multiple sum \[Sum]_n ...

Applying transformation rules. The replacement operator /. (pronounced "slash-dot") applies rules to expressions. You can give a list of rules to apply. Each rule will be ...

Mathematica normally makes as few assumptions as possible about the objects you ask it to manipulate. This means that the results it gives are as general as possible. But ...

Integrate[f, x] gives the indefinite integral \[Integral]f d x. Integrate[f, {x, x_min, x_max}] gives the definite integral \[Integral]_x_min^x_max\ f\ d x. Integrate[f, {x, ...

StieltjesGamma[n] gives the Stieltjes constant \[Gamma]_n. StieltjesGamma[n, a] gives the generalized Stieltjes constant \[Gamma]_n (a).

TrigToExp[expr] converts trigonometric functions in expr to exponentials.

FindIntegerNullVector[{x_1, x_2, ..., x_n}] finds a list of integers a_i such that a_1 x_1 + a_2 x_2 + \[CenterEllipsis] + a_n x_n == 0. FindIntegerNullVector[{x_1, x_2, ..., ...

The general solution to this equation is found by separation of variables. Even when variables can be separated, the final solution might be accompanied by a warning message ...

Numerical root finding. NSolve gives you numerical approximations to all the roots of a polynomial equation. You can also use NSolve to solve sets of simultaneous equations ...

Now that we have introduced the basic features of patterns in Mathematica, we can use them to give a more or less complete example. We will show how you could define your own ...