Defining Numerical Values
If you make a definition such as , Mathematica will use the value you give for any function it encounters. In some cases, however, you may want to define a value that is to be used specifically when you ask for numerical values.
expr=value define a value to be used whenever possible
N[
expr]=
value define a value to be used for numerical approximation
Defining ordinary and numerical values.
This defines a numerical value for the function .
Defining the numerical value does not tell Mathematica anything about the ordinary value of .
If you ask for a numerical approximation, however, Mathematica uses the numerical values you have defined.
You can define numerical values for both functions and symbols. The numerical values are used by all numerical
Mathematica functions, including
NIntegrate ,
FindRoot , and so on.
N[
expr]=
value define a numerical value to be used when default numerical precision is requested
N[
expr,{
n,
Infinity}]=
value define a numerical value to be used when n-digit precision and any accuracy is requested
Defining numerical values that depend on numerical precision.
This defines a numerical value for the symbol , using terms in the product for -digit precision.
Here is the value of , computed to 30-digit precision using the value you specified.
Mathematica treats numerical values essentially like upvalues. When you define a numerical value for
f,
Mathematica effectively enters your definition as an upvalue for
f with respect to the numerical evaluation operation
N .