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BUILT-IN MATHEMATICA SYMBOL
Function 
Function[body]
or body& is a pure function. The formal parameters are 
(or 
), 
, etc.
Function[x, body]
is a pure function with a single formal parameter x.
Function[{x1, x2, ...}, body]
is a pure function with a list of formal parameters.
Details
- When Function[body] or body& is applied to a set of arguments,
(or 
) is replaced by the first argument, 
by the second, and so on. 
is replaced by the function itself. - If there are more arguments supplied than #i in the function, the remaining arguments are ignored. »
stands for the sequence of all arguments supplied. »- ##n stands for arguments from number n onward. »
- Function[x, body] can be input as
, where the character 
is entered as EscfnEsc or \[Function]. - Function is analogous to
in LISP or formal logic. - Function has attribute HoldAll. The function body is evaluated only after the formal parameters have been replaced by arguments.
- The named formal parameters
in Function[{x1, ...}, body] are treated as local, and are renamed 
when necessary to avoid confusion with actual arguments supplied to the function. » - Function constructs can be nested in any way. Each is treated as a scoping construct, with named inner variables being renamed if necessary. »
- Function[params, body, {attr1, attr2, ...}] represents a pure function that is to be treated as having attributes
for the purpose of evaluation. »
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