InverseSeries[s] takes the series s, and gives a series for the inverse of the function represented by s. InverseSeries[s, x] uses the variable x in the inverse series.

MultiplicativeOrder[k, n] gives the multiplicative order of k modulo n, defined as the smallest integer m such that k^m \[Congruent] 1 mod n. MultiplicativeOrder[k, n, {r_1, ...

PartitionsP[n] gives the number p (n) of unrestricted partitions of the integer n.

RegionFunction is an option for plotting functions that specifies the region to include in the plot drawn.

AccuracyGoal is an option for various numerical operations which specifies how many effective digits of accuracy should be sought in the final result.

PrecisionGoal is an option for various numerical operations which specifies how many effective digits of precision should be sought in the final result.

EconomizedRationalApproximation[expr, {x, {x_0, x_1}, m, n}] gives the economized rational approximation to expr that is good over the interval x_0 to x_1, with numerator ...

Numerical sums and products. This gives a numerical approximation to ∑_(i=1)^∞((1)/(i^3+i!)). There is no exact result for this sum, so Mathematica leaves it in a symbolic ...

NecklacePolynomial[n, c, Cyclic] returns a polynomial in the colors in c whose coefficients represent numbers of ways of coloring an n-bead necklace with colors chosen from ...

New functions SymmetricPolynomial and SymmetricReduction have been added to the built-in Mathematica kernel.