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
.
| Out[2]= |  |
If you ask for a numerical approximation, however,
Mathematica uses the numerical values you have defined.
| Out[3]= |  |
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.
| Out[5]= |  |
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.
