For the exact argument , Mathematica returns an exact result.
For a machine‐number argument (numerical argument with a decimal
point), a machine number is also returned. The next inputs
calculate 100‐digit approximations at and . It is possible to
calculate thousands of digits for the hyperbolic secant function
in less than a second. The next input calculates 10000 digits
for and analyzes the frequency of the digit in the resulting
decimal number. Here is a 50‐digit approximation to the
hyperbolic secant function at the complex argument . Mathematica
automatically evaluates mathematical functions with machine
precision, if the arguments of the function are numerical values
and include machine‐number elements. In this case, only six
digits after the decimal point are shown in the results. The
remaining digits are suppressed, but can be displayed using the
function InputForm. Mathematica knows the symmetry and
periodicity of the hyperbolic secant function. Here are some
examples. Mathematica automatically simpl