Jump to content

Wikipedia:Reference desk/Archives/Mathematics/2013 January 23

From Wikipedia, the free encyclopedia
Mathematics desk
< January 22 << Dec | January | Feb >> January 24 >
Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.


January 23

[edit]

website regarding numbers like 13.7 billion

[edit]

Is there a website that shows the numbers in digit form like 13.7 billion? Thanks. --Donmust90 (talk) 01:10, 23 January 2013 (UTC)Donmust90 — Preceding unsigned comment added by Donmust90 (talkcontribs) 00:56, 23 January 2013 (UTC)[reply]

Do you mean:
1) 13,700,000,000
Or:
2) 1.37 × 1010 ? StuRat (talk) 01:20, 23 January 2013 (UTC)[reply]
Either way, Wolfram Alpha at http://www.wolframalpha.com/ expands the term into both normal and scientific notation. --Stephan Schulz (talk) 01:31, 23 January 2013 (UTC)[reply]

Hmm, the only thing that should be added is to note that 'billion' can be an ambiguous term - in some contexts 10^9, others 10^12 ---- nonsense ferret 02:20, 23 January 2013 (UTC)[reply]

Yeah, but the 10^12 meaning is almost obsolete in English. When The Economist started using the "short billion", the game was over. --Trovatore (talk) 02:23, 23 January 2013 (UTC)[reply]
Yes, Harold Wilson was responsible for changing the meaning of "billion" in the UK, but the 10^12 (million million) meaning cannot be obsolete whilst I still use it (in common with most of the European continent who have a similar word). Dbfirs 07:57, 24 January 2013 (UTC)[reply]
I did say "almost". I also said in English, which makes the point about Continental Europe irrelevant. --Trovatore (talk) 09:25, 24 January 2013 (UTC)[reply]
OK, point taken, though millions (not billions) in Continental Europe do speak English to some extent. Dbfirs 08:22, 25 January 2013 (UTC)[reply]

Is there a closed form expression for this quantity?

[edit]

where the sum is taken over all K-dimensional vectors whose entries are nonnegative integers which sum to ? --AnalysisAlgebra (talk) 16:20, 23 January 2013 (UTC)[reply]

If K > 1 and A is a positive integer, the answer is . There always will be an entry equal to 0.
So you may have meant to say that the components of the vectors are positive integers (but then I don't know the answer to the question). Icek (talk) 16:41, 23 January 2013 (UTC)[reply]
(Assuming positive integers, as pointed out by Icek.) Already for K = 2, the sum equals
where Hn is the nth harmonic number. There is no closed-form expression for that under the usually understood meanings of “closed-form”.—Emil J. 17:05, 23 January 2013 (UTC)[reply]