GammaRegularized[a, z] is the regularized incomplete gamma function Q(a, z).

HypergeometricPFQ[{a_1, ..., a_p}, {b_1, ..., b_q}, z] is the generalized hypergeometric function \[Null]_p F_q (a; b; z).

PolyGamma[z] gives the digamma function \[Psi](z). PolyGamma[n, z] gives the n\[Null]^th derivative of the digamma function \[Psi] (n) (z).

PolyLog[n, z] gives the polylogarithm function Li_n (z).PolyLog[n, p, z] gives the Nielsen generalized polylogarithm function S n, p (z).

lhs := rhs assigns rhs to be the delayed value of lhs. rhs is maintained in an unevaluated form. When lhs appears, it is replaced by rhs, evaluated afresh each time.

Some operators used in basic arithmetic and algebra. Note that the  for ∖[Cross] is distinguished by being drawn slightly smaller than the × for ∖[Times]. Interpretation of ...

Series[f, {x, x_0, n}] generates a power series expansion for f about the point x = x_0 to order (x - x_0) n. Series[f, {x, x_0, n_x}, {y, y_0, n_y}, ...] successively finds ...

Compile[{x_1, x_2, ...}, expr] creates a compiled function that evaluates expr assuming numerical values of the x_i. Compile[{{x_1, t_1}, ...}, expr] assumes that x_i is of a ...

When fitting models to data, it is often useful to analyze how well the model fits the data and how well the fitting meets the assumptions of the model. For a number of ...

Mathematica has a collection of commands that do unconstrained optimization (FindMinimum and FindMaximum) and solve nonlinear equations (FindRoot) and nonlinear fitting ...