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 <math>{d \over dx} e^x = e^x<math>. 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 <math>xy = yx<math> (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)