Gamma[z] is the Euler gamma function \[CapitalGamma](z). Gamma[a, z] is the incomplete gamma function \[CapitalGamma](a, z). Gamma[a, z_0, z_1] is the generalized incomplete ...

Piecewise[{{val_1, cond_1}, {val_2, cond_2}, ...}] represents a piecewise function with values val_i in the regions defined by the conditions cond_i. Piecewise[{{val_1, ...

Simplify[expr] performs a sequence of algebraic and other transformations on expr, and returns the simplest form it finds. Simplify[expr, assum] does simplification using ...

In general, a system of ordinary differential equations (ODEs) can be expressed in the normal form, The derivatives of the dependent variables x are expressed explicitly in ...

Patterns stand for classes of expressions. They contain pattern objects that represent sets of possible expressions. Pattern objects. When several pattern objects with the ...

Mathematica includes all the common special functions of mathematical physics found in standard handbooks. Each of the various classes of functions is discussed in turn. One ...

In any interactive session, Mathematica effectively operates in a loop. It waits for your input, processes the input, prints the result, then goes back to waiting for input ...

Newton's method for nonlinear equations is based on a linear approximation so the Newton step is found simply by setting M_k(p)=0, Near a root of the equations, Newton's ...

Histogram[{x_1, x_2, ...}] plots a histogram of the values x_i.Histogram[{x_1, x_2, ...}, bspec] plots a histogram with bin width specification bspec.Histogram[{x_1, x_2, ...

Mathematica has over 3000 built-in functions and other objects, all based on a single unified framework, and all carefully designed to work together, both in simple ...