Defining Numerical Values
If you make a definition such as
f[x_]:=value,
Mathematica will use the value you give for any
f 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 f. |
Defining the numerical value does not tell Mathematica anything about the ordinary value of f.
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If you ask for a numerical approximation, however, Mathematica uses the numerical values you have defined.
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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 const, using 4n+5 terms in the product for n-digit precision. |
Here is the value of const, computed to 30-digit precision using the value you specified.
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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.
