Using original algorithms developed at Wolfram Research, Mathematica evaluates error and exponential integral functions anywhere in the complex plane, to arbitrary ...

The built-in Mathematica iteration functions such as Table and Sum evaluate their arguments in a slightly special way. When evaluating an expression like Table[f,{i,i_max}], ...

DifferentialRootReduce[expr, x] attempts to reduce expr to a single DifferentialRoot object as a function of x.DifferentialRootReduce[expr, {x, x_0}] takes the initial ...

Mathematica transparently works with complex variables throughout, not only numerically, but also symbolically—often relying on original results to handle intricate branch ...

Mathematica allows you to define transformation rules for any expression. You can define such rules not only for functions that you add to Mathematica, but also for intrinsic ...

Many programs you write will involve operations that need to be iterated several times. Nest and NestList are powerful constructs for doing this. Applying functions of one ...

Although Mathematica matches patterns in a purely structural fashion, its notion of structural equivalence is quite sophisticated. In particular, it takes account of ...

Mathematica has a wide coverage of named functions defined by sums and recurrence relations. Often using original algorithms developed at Wolfram Research, Mathematica ...

RootLocusPlot[g, {k, k_min, k_max}] generates the root locus plot of a rational function g of k ranging from k_min to k_max.RootLocusPlot[sys, ...] plots the root loci of a ...

Mathieu and related functions. The Mathieu functions MathieuC[a,q,z] and MathieuS[a,q,z] are solutions to the equation y^′′+[a-2qcos(2z)]y0. This equation appears in many ...