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.