Talk:List of mathematical functions

From Wikipedia, the free encyclopedia

Contents

[edit] Elementary functions

Floor function and Signum function are not elementary functions. --fil

I'm pretty sure they're not special functions either; at least I've never seen them discussed as such. (Special function has a specific connotation if not an exact definition.) Wikipedia's own special function article doesn't mention them, nor do a couple of others I looked at. http://en.wikipedia.org/wiki/Special_functions http://www.math.com/tables/integrals/specialfuns.htm
http://mathworld.wolfram.com/SpecialFunction.html --starwed

[edit] Periodic and transcendental functions

1. I've seen that the trigonometric functions are moved back and forth between the periodic and and transcendental functions. It's clear that they belong both, but it seems odd right now when they appear twice. Can someone suggest how and where to put them?

2. Are the inverse trigonometric functions (e.g. arcsine) formally included in trigonometric functions, or should be specified separately?

3. For Power functions, should it be specified that the power is not integer? Yoshigev 14:33, 24 February 2006 (UTC)

  • Periodic and transcendental are overlapping categories indeed. What's wrong with including a function in both?
  • Right: xn is not transcendental for integer n (and how about rational n?)
  • As far as I gather from the definitions square root isn't transcedental
we should add a group algebraic functions −Woodstone 22:06, 24 February 2006 (UTC)
  • Yes, I think we should add algebraic functions, and below it put: the polynomials, rational functions, square root, and rational powers (radical functions).
  • All periodic functions are transcendental (except functions like f(x)=a), so I think they should be put them under "transcendental functions".
  • Since all the functions are either algebraic or transcendental, I think that we should also put the functions at the beginning of the section into these sub-sections.
—Yoshigev 21:40, 25 February 2006 (UTC)
  • What's more, hyperbolic functions are periodic too (of imaginary period however). Xedi 13:06, 30 March 2006 (UTC)

[edit] Odd mix in categories

The first few categories of functions are a rather odd grouping. We might distinguish properties definable based on:

  • set theory
  • a single operation (+ or *)
  • a group structure
  • two operations (both + and *)
  • on a field structure
  • the real numbers
  • the complex numbers

−Woodstone 12:19, 25 February 2006 (UTC)

I have now made a first try at more structure. Since there is a lot of overlap between categories it is not fully satisfying yet. Your comments (and edits) are welcome. −Woodstone 22:15, 25 February 2006 (UTC)

I think "Function classification property" should only list properties, so the functions in "Relative to a field" should be under elementry functions. The same with "Number theoretic functions" that should be in a different section.
Do you think that it's important to distinguish between "real" and "real (or complex)"? —Yoshigev 00:26, 26 February 2006 (UTC)
I am not sure about "Relative to a topology". I found that there are two definitions for continuity: Continuous function, Continuous function (topology). I don't think that the normal continuity should be under topology, so maybe in the same category with monotonic function, under "real analysis" (see List of real analysis topics). —Yoshigev 15:18, 26 February 2006 (UTC)

I have tried to classify the functions according to the minimum requirements on their domain (and codomain). Continuity can be defined on a topological space. Every metric space (like the real or complex numbers) is also a topological space. The continuity in such a space is the same as the one defined for the induced topology (the article mentions this vaguely).

The functions under "field" do not require the function to be real/complex. Perhaps the number theoretic functions can be mover under this heading (but I'm not expert enough to be sure).

The functions under "real" cannot be (usually are not) defined for the complex plane.

As far as I have checked, all functions under "special" are real/complex functions. −Woodstone 15:45, 26 February 2006 (UTC)

Right now it looks like a jumble of all the functions. First of all, I think we should divide between function properties (like "Injective function") and function classes (like "Polynomials").
After that, I suggest that the article will have this sections:
  • Elementry functions (like polynomials and trig). Divided to:
    • Algebraic
    • Trancendental (with maybe what is now under "Relative to an integral domain", but I'm not sure).
  • Special functions (Gamma, Elliptic...)
  • Function properties (with the division of Woodstone).
I think most readers would look for elementry functions in this aricle so they should appear first.
—Yoshigev 14:51, 1 March 2006 (UTC)

It's already much better than it was before, but you're welcome with further improvement suggestions (and actions). A few remarks to your remarks: most of the "special" functions and the "trig" functions are transcendental, so your the grouping proposed above needs some work. I'm not so sure what was meant by "integral domain" (I called it a "ring" structure). Perhaps we should go back to the "number theory" group. −Woodstone 16:32, 1 March 2006 (UTC)

I've made the change in the sectioning. But there are still functions that I don't really know where to put.
  • I think that most functions under "Basic special functions" are elementary, but I'm not sure. If somebody can sort them, and find a nice heading for them...
  • I think that "Relative to an integral domain (number theory)" should be put under "special functions", but again I'm not sure.
—Yoshigev 18:59, 1 March 2006 (UTC)

I moved some specific functions (such as the number theoretic ones) into "special functions", and some lines that were actually properties of functions (differentiable, homomorphic, analytic) into the categories. I think there is no real definition of "basic" or "elementary" functions, that is just a school term. −Woodstone 21:35, 1 March 2006 (UTC)

The article define elementary function by giving a list of operation that construct them. I didn't find any name for them, and didn't want to give the whole list, so I wrote "basic operation". I put all the other functions under "special" although some of them don't fully qualify the term (like Absolute value).
You moved the following functions to the properties section but I think they are specific functions (not a class): Dirichlet function, Question mark function, Weierstrass function.
—Yoshigev 10:35, 2 March 2006 (UTC)

I agree that "Question mark function" and "Weierstrass function" are specific, but "Dirichlet function" is a class. Feel free to move accordingly. −Woodstone 12:19, 2 March 2006 (UTC)

[edit] Should this even be here?

This list is so completely incomplete it shouldn't even be here.

A list like this could by definition never be complete. That does not mean that it is of no interest. If important named functions are missing, why not add them? −Woodstone 21:37, 4 October 2006 (UTC)

[edit] Dawson function

The Dawson function is listed twice (under both "Antiderivatives of elementary functions" and "Other standard special functions") 141.228.106.135 (talk) 09:15, 18 April 2008 (UTC)

I've removed the second mention. Gandalf61 (talk) 09:44, 18 April 2008 (UTC)