A.3.10 Mathematical Functions

The mathematical functions such as Log[x] and BesselJ[n, x] that are built into Mathematica have a number of features in common.

• They carry the attribute Listable, so that they are automatically "threaded" over any lists that appear as arguments.
• They carry the attribute NumericFunction, so that they are assumed to give numerical values when their arguments are numerical.
• They give exact results in terms of integers, rational numbers and algebraic expressions in special cases.
• Except for functions whose arguments are always integers, mathematical functions in Mathematica can be evaluated to any numerical precision, with any complex numbers as arguments. If a function is undefined for a particular set of arguments, it is returned in symbolic form in this case.

• Numerical evaluation leads to results of a precision no higher than can be justified on the basis of the precision of the arguments. Thus N[Gamma[27/10], 100] yields a high-precision result, but N[Gamma[2.7], 100] cannot.
• When possible, symbolic derivatives, integrals and series expansions of built-in mathematical functions are evaluated in terms of other built-in functions.