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I came along the following function definition

f[a_, b_, c_][r_] = ...

with some function on the right hand side. Is this equivalent to

f[a_, b_, c_,r_] = ...

or

f[{a_, b_, c_},r_] = ...

?

If so, what are the advantages or field of use of these different definitions? Are there more possibilities?

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marked as duplicate by ciao, bbgodfrey, C. E., Daniel Lichtblau, Dr. belisarius Mar 31 '15 at 16:08

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ No, these are not equivalent. Why don't you try the different forms and discover the differences. Great way to make the learning stick. $\endgroup$ – ciao Mar 31 '15 at 14:00
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    $\begingroup$ Possible duplicates here and here $\endgroup$ – ciao Mar 31 '15 at 14:11
  • $\begingroup$ agree @ rasher, with trying the different forms this I have tried to convey in my answer to encourage @wondering. $\endgroup$ – penguin77 Mar 31 '15 at 19:02
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Example 3 is very different from example 1 and 2.

Example 2 is a function with 4 arguments whereas example 3 has two arguments, first argument is a list with three elements{a_,b_,c_} and 2nd argument is r.

Function names are in Mathematica not only defined by their names but by their name,structure of arguments and the names of the arguments.

Comparing example 1 and 2, they both called like a function with 4 arguments. Example 1 with the double brackets works because function definition are stored as rules in Mathematica and evaluated by the kernel's pattern matching engine. However example 1 seems awakened to me, because it complicates the syntax without adding any benefit.

Let's have a look how the tree examples are being called by a Pure function:

Example 1:

f[a_, b_, c_][r_] := a b c^r
f[#1, #2, #3][#4] &[1, 2, 3, 4]
(* 162 *)

Example 2:

 f[a_, b_, c_,r_] := a b c^r
    f[#1, #2, #3,#4] &[1, 2, 3, 4]
    (*162*)

Example 3:

 f[{a_, b_, c_},r_] := a b c^r
    f[#1, #2] &[{1, 2, 3}, 4]
    (*162*)

In general it is preferable to limit the number of arguments for a function to a minimum necessary. Example 1, even that it works technically is not very readable in the code and I would recommend to avoid it.

Hint: The corresponding rules processed by the Mathematica kernel can be revealed using DownValues. For example

fn[a_, b_, c_, r_] := a+b+c+r
DownValues[fn]

(* {HoldPattern[fn[a_, b_, c_, r_]] :> a+b+c+r} *)

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