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I'm an engineer/physicist by training, and typically, my publications are in journals where the readers do have an semi-advanced understanding of math, but not at a serious mathematician's level. So often, when I use some transform or a function that is not known to the community, I'd like to point them to a reference that's precise, yet simple to read and readily accessible. It seems unfair to point them towards a dense article/book that might be the best in the field, yet completely useless to someone reading my paper.

What I'm looking for, would be an online form of the Encyclopedic Dictionary of Mathematics (EDM), which is a remarkable reference. This is my favourite option, but I'd like to know if there are online alternatives (by a trusted body, not a run of the mill math-o-pedias that float around), which makes access easier.

One that comes to mind is Wolfram MathWorld (WM), which although impressive, can be lacking at times (to put it this way, they have very good references on mathematical concepts that Mathematica is capable of doing). The Digital Library of Mathematical Functions (DLMF) is not bad either, but doesn't come close to the EDM.

Lastly, Wikipedia (WP) is pretty decent, especially in conveying concepts to the lay reader. However the anyone-can-edit it feature makes it a little less reliable than the other three.

For now, my feeling is that EDM $\gt$ WM $\approx$ DLMF $\geq$ WP. Do you have suggestions?

If you think otherwise of my rating of the references, please do let me know why... perhaps I might have overlooked a few aspects in evaluating them and am open to reviewing them.

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4 – yoyo Apr 15 '11 at 1:14
For the things that are actually in DLMF, I would almost certainly rank it above WM. For mathematical concepts, the EOM that yoyo suggests is perhaps the best resource, though for specific transform/function, the EOM may not be all that different from just reading a book. – Willie Wong Apr 15 '11 at 10:54
I don't believe anybody has attempted to make a compilation, much less an update, of the stuff on (integral and other) transforms in the Bateman papers... that would make for an interesting project, I reckon. And yes, I too would rate DLMF quite a bit above MathWorld. The Wolfram Functions site has stuff that the DLMF doesn't have, but not much. – J. M. Apr 16 '11 at 17:28
@yoyo: Thanks for that link. It looks like a pretty well maintained encyclopedia, and will probably replace most of my online options. If you post that as an answer, I'll accept it. – user4423 Apr 17 '11 at 20:30
If you read Japanese, the most recent (Japanese 4th) edition of the Encyclopedic Dictionary of Mathematics has an accompanying CD-ROM that contains PDF files of the 4th and 3rd (equivalent to English 2nd) edition, which I find extremely convenient. (But of course they are not for free.) – pharmine Nov 7 '11 at 20:11

Other than wikipedia, there's wolfram's site and there's also a free collaborative encyclopedia at

share|cite|improve this answer is the most comprehensive online mathematics resource I have found. It is also extremely reliable, although at times a little opaque.

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I agree and I like wikipedia. However, it certainly won't meet the standards in a peer reviewed journal specifically because it can be edited at will, and what I cite might not be what the reader views. – user4423 Apr 15 '11 at 3:35
Agreed, it's no source for peer reviewed mathematics. A good place to start finding peer reviewed info would be mathscinet or something, I guess. – Jon Beardsley Apr 15 '11 at 4:18
@yoda: it is possible to cite any particular revision of some article. Have a look at the history tab of some article. – Francesco Turco Apr 15 '11 at 7:06

If you're talking about Laplace transforms or other things then I wouldn't know of texts that have simple explanations to what they mean, in fact only by going through the mess of doing it can one understand even a bit of what's being said. So ultimately it depends on how much your readers do want to understand.

Since you're an engineer/physicist by training, you deal with a lot of differential equations so I suggest Morris and Tenenbaum's Ordinary Differential Equations, it's a great book and furthermore it's for students of science and engineering, I use it for my differential equations class.

In fact the chapter on Laplace Transforms is not hard at all, great for a quick reference.

But if you're invoking stuff from complex analysis then 100% I would suggest Needham's Visual Complex Analyis, it's not even that complicated and it's full of pictures that illustrate beautifully what's happening!

Good luck in finding what you need, Ben

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I don't think Laplace falls under "transform or a function that is not known to the community" – Daenerys Naharis Apr 15 '11 at 1:46
Thanks for your comments. I'm not looking for physical references (books)... I have good references for those. I was specifically looking for online resources. – user4423 Apr 15 '11 at 3:33

The Princeton companion to mathematics is also available online if you have an Ebrary subscription.

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