Talk:Exponential function

Aren't there multiple forms of the exponential function? Specifically, isn't the most general form ka^bx ? Admittedly, the differences can be incorporated in to b thus: ke^bxln(a), but wouldn't the first form be more clear to the laymen?

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You don't really need the b; the most general form is ka^x. I mention these in the "science" paragraph; they are indeed the most useful to the "laymen". However they cannot be defined without exp(x) and in mathematics, exp(x) is tremendously more important than a^x, so I started the article with exp(x) and then came to a^x as soon as possible. --AxelBoldt

I've changed the opening paragraphs to introduce the form ka^x even sooner. - dcljr 12:50, 6 Aug 2004 (UTC)

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It shouldn't read: The graph of ex does not ever touch the x axis, although it comes very close.

but rather: The graph of ex does not ever touch the x axis, although it comes arbitrarily close (in a limit sense).

Coherent Graphs

Many of the math articles have graphs in smooth brown, using the same design all over. (Other colors also exist, like in the article Taylor expansion.) How are these graphs created? Interesting to anyone starting a new maths article. -- Sverdrup 22:40, 9 Dec 2003 (UTC)

The graphs were written in Java, and copied from the screen. The code is at User:Cyp/Java. Κσυπ Cyp   01:27, 10 Dec 2003 (UTC)

My edits of Aug 6, 2004

I just made a major edit to this article. Mostly small changes, but some major.

• Added a section heading earlier in the article so the table of contents will (most likely) be "above the fold".
• Rearranged things to put off non-real variables as long as possible. I think this will benefit readers who are less mathematically experienced.
• Right-aligned the graph again (see page history). What's wrong with having it right-alinged?
• Consistently replaced <i>italics</i> with ''wikitalics''.
• Included multiple interpretations of ${d \over dx}e^{x}=e^{x}$. I know they're redundant, but that's the point: to say it in ways that might be more familiar to the reader. A picture would be particularly helpful here, I think.
• Removed mention of "linear ordinary differential equations" in the similarly named section; if you think it's crucial, add it back (see page history).
• Removed parenthetical remark in "Banach algebras" section:

if $xy=yx$ (we should add the general formula involving commutators here.)

After much struggle, I decided not to change anything else of substance in that section or the next one on Lie algebras. I don't trust my understanding of these things (or lack thereof). Speaking of the "Lie groups" section, someone should probably try to make it more clear.

Oh, and BTW: Do we really need the same properties listed 3 times? I know we're talking about different mathematical objects at different places in the article, but still, I find it kinda redundant. Couldn't we name or number the properties and refer to them that way?

- dcljr 12:43, 6 Aug 2004 (UTC)

information should be reordered

IMHO,

• the very first paragraph should be as short as possible for several reasons
  • editing it makes it necessary to edit the whole page, which may become impossible at some point. So it should only contain things that are absolutely necessary and which will (almost) certainly never need any modification.
  • it lessens the usefulness of the "Contents" table, which should come before any detailed information, except for a minimalistic explanation of "what is this page about" and "what is found elsewhere".
• there are too many details about the graph of the exp function in the 1st paragraph (postitive with explanation, increasing with explanation), and still its not complete (convexity, asymptotics, ...). The picture itself is enough on top of the article, as it contains all that information.
• It is strange to have the (body of the) article start with "Properties" instead of an (even informal) definition.
• It is even more strange to have the "Properties" to start with a generalization of the exp function.

MFH 15:07, 8 Apr 2005 (UTC)

very strange

It is taught in China that y = a to the x-th power is the standard definition of exponential function, while y = e to the x-th power is just a particular case of exponential functions. Got confused when try to translate this article to zh.wikipedia.org.

See exponentiation Bo Jacoby 16:36, 23 October 2005 (UTC)

But this is the article about THE exponential fucntion. AN exponential fuction is y=a^x (which can be derived from THE exponential function by imputting x=ln(a)x). I would therefore agree with China's definition of AN exponential function.--Hypergeometric2F1[a,b,c,x] 11:03, 20 December 2005 (UTC)

Comment moved from article

Moved from top of article [The definition below is incomplete and not rigorous (Paulo Eneas, SP, Brazil)] (Enchanter 22:09, 26 November 2005 (UTC))

Title change

This article should be named "The Exponential Function" or at least there should be a disambiguation page differentiating this from "AN Exponential Function" f(x)=a^x, to avoid possible confusion.--Hypergeometric2F1[a,b,c,x] 11:06, 20 December 2005 (UTC)

I disagree with the move to "The exponential function". Maybe something more can be said about the general a^x function in addition to what already is in here. Oleg Alexandrov (talk) 21:34, 21 December 2005 (UTC)

If the article were to be moved it should be named the natural exponential function in accord with the term "natural logarithm" (a logarithm can be based on any exponential function in the form a^x, e^x is special because of his "natural" properties). --Friðrik Bragi Dýrfjörð 16:30, 27 April 2006 (UTC)

sin⁻¹x is ambiguous

There is no need for a shorthand of this kind for reciprocal trigonometric functions since they each have their own name and abbreviation already: (sin x)^-1 is normally just written as csc x.

Actually, also the arcsine has its own abbreviaton, i.e. arcsin x. And sin⁻¹x is sometimes used to mean 1/sin x. Then we have cscx and arcsinx, which are both unambiguous, whereas sin⁻¹x is ambiguous. See Trigonometric functions#Inverse function. I personally never use the notation sin⁻¹x to avoid misunderstandings. But the current wording implies that it always refers to the arcsine. (And by the way, I've seen the notation fⁿx for any functions denotated by a string of lowercase latin characters, e.g. log²x to mean (logx)² rather than log logx. --Army1987 20:41, 10 March 2006 (UTC)