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I cannot understand why Zeta[0] is -1/2. One would think that it is infinity but obviously this is not the case. 69.120.50.249 ( talk) 01:45, 19 June 2009 (UTC)
What is the definition for other values? —Preceding unsigned comment added by 69.120.50.249 ( talk) 02:01, 19 June 2009 (UTC)
While punching buttons on my calculator recently, I noticed that (using Mathematica syntax):
Integrate[x^x,{x,0,1}] ≈ 0.783430510909
and
-Sum[(-x)^(-x),{x,1,Infinity}] ≈ 0.783430510712.
I was wondering: is this near-miss a near miss because they are actually the same and the calculator is making rounding errors, or is it a near-miss because the integral and the sum actually give different results?
If it helps, the calculator is a TI-89 Titanium, OS version 3.0, hardware version 4.0. -- 72.197.202.36 ( talk) 02:42, 19 June 2009 (UTC)
Does anybody know a nice, closed-form way of generating Bernoulli numbers? I.e., Bn = what? -- 72.197.202.36 ( talk) 03:59, 19 June 2009 (UTC)
If no such method is available, are there any relatively simple algorithms to generate them? -- 72.197.202.36 ( talk) 04:00, 19 June 2009 (UTC)
Akiyama-Tanigawa algorithm for Bn | ||||||||
Enter integer n. For m from 0 by 1 to n do
|
The question may have been inspired by the news story Iraq-born teen cracks maths puzzle which begins
From the generating function formula it follows that which has the closed form the OP was asking for: Bn = what?. But perhaps the OP is not happy because the intermediate results are functions rather than numbers. Bo Jacoby ( talk) 15:57, 20 June 2009 (UTC).
knowing that the coefficient of friction between the 25kg block and the incline is 0.25 determine the value of p for which motion of block up the inclined plane is impending —Preceding unsigned comment added by 81.199.50.67 ( talk) 12:32, 19 June 2009 (UTC)
Is it automatically unphysical to have a PCA reconstruction that has some stations negatively weighted? Note, that this is more than just a PCA, but PCA followed by some regressions. Would think that it could occur for both degeneracy and anticorrelation with the average (actual physical effects). Of course the summation must be positive, but is it automatically wrong if some of the stations have negative weights?
This is being debated on these blog threads. Unfortunatley, the debate has muddled particular examination of the Stieg Antarctic PCA-based recon with general absolute claims that negative weightings are bad, bad, bad.
Could you please adjuticate?
See here:
http://noconsensus.wordpress.com/2009/06/07/antarctic-warming-the-final-straw/#comment-6727
http://noconsensus.wordpress.com/2009/06/09/tired-and-wrong-again/#comment-6726
http://wattsupwiththat.com/2009/06/10/quote-of-the-week-9-negative-thermometers/#more-8362
http://www.climate-skeptic.com/2009/06/forgetting-about-physical-reality.html
Would appreciate some reference to a citation or an academician and/or a more in-depth answer than just "he or she is right" so that I can either get my opponent to understand where he is wrong, or understand it myself. Muchos gracias.
69.250.46.136 (
talk)
18:00, 19 June 2009 (UTC)
Hi. I'm halfway through working out the answer to a question and am now stuck. Here's what I have
"Let where n is a positive integer and . Find an expression for the largest root of the equation f(x)=0, distinguishing between the cases where n is even and n is odd. You may assume that ."
So after working through this I get solutions as follows:
provided
provided
provided
provided
where p is some integer.
First of all, is what I have correct? Secondly, how do you distinguish between odd and even? I can't see what difference it will make to my answer. Thanks asyndeton talk 20:51, 19 June 2009 (UTC)
Let u = 2nx. Then the function is
and this is 0 iff either sin u = 0 (so u is an integral multiple of π) or cos u = either 1 or −1/2 (so that u is an integral multiple of 2π/3).
The condition that x is between 0 and π/2 says that u is between 0 and nπ.
If n is even then the largest multiple of 2π/3 that is less than nπ is π(n − 2/3). If n is odd, then put "1/3" there instead of "2/3". (Just draw the picture on the x-axis with n going from 0 to about 5 or so, and you'll see it. Never mind what the curve looks like; just graph the zeros as I described them above.) Michael Hardy ( talk) 21:44, 19 June 2009 (UTC)
Mathematics desk | ||
---|---|---|
< June 18 | << May | June | Jul >> | June 20 > |
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. |
I cannot understand why Zeta[0] is -1/2. One would think that it is infinity but obviously this is not the case. 69.120.50.249 ( talk) 01:45, 19 June 2009 (UTC)
What is the definition for other values? —Preceding unsigned comment added by 69.120.50.249 ( talk) 02:01, 19 June 2009 (UTC)
While punching buttons on my calculator recently, I noticed that (using Mathematica syntax):
Integrate[x^x,{x,0,1}] ≈ 0.783430510909
and
-Sum[(-x)^(-x),{x,1,Infinity}] ≈ 0.783430510712.
I was wondering: is this near-miss a near miss because they are actually the same and the calculator is making rounding errors, or is it a near-miss because the integral and the sum actually give different results?
If it helps, the calculator is a TI-89 Titanium, OS version 3.0, hardware version 4.0. -- 72.197.202.36 ( talk) 02:42, 19 June 2009 (UTC)
Does anybody know a nice, closed-form way of generating Bernoulli numbers? I.e., Bn = what? -- 72.197.202.36 ( talk) 03:59, 19 June 2009 (UTC)
If no such method is available, are there any relatively simple algorithms to generate them? -- 72.197.202.36 ( talk) 04:00, 19 June 2009 (UTC)
Akiyama-Tanigawa algorithm for Bn | ||||||||
Enter integer n. For m from 0 by 1 to n do
|
The question may have been inspired by the news story Iraq-born teen cracks maths puzzle which begins
From the generating function formula it follows that which has the closed form the OP was asking for: Bn = what?. But perhaps the OP is not happy because the intermediate results are functions rather than numbers. Bo Jacoby ( talk) 15:57, 20 June 2009 (UTC).
knowing that the coefficient of friction between the 25kg block and the incline is 0.25 determine the value of p for which motion of block up the inclined plane is impending —Preceding unsigned comment added by 81.199.50.67 ( talk) 12:32, 19 June 2009 (UTC)
Is it automatically unphysical to have a PCA reconstruction that has some stations negatively weighted? Note, that this is more than just a PCA, but PCA followed by some regressions. Would think that it could occur for both degeneracy and anticorrelation with the average (actual physical effects). Of course the summation must be positive, but is it automatically wrong if some of the stations have negative weights?
This is being debated on these blog threads. Unfortunatley, the debate has muddled particular examination of the Stieg Antarctic PCA-based recon with general absolute claims that negative weightings are bad, bad, bad.
Could you please adjuticate?
See here:
http://noconsensus.wordpress.com/2009/06/07/antarctic-warming-the-final-straw/#comment-6727
http://noconsensus.wordpress.com/2009/06/09/tired-and-wrong-again/#comment-6726
http://wattsupwiththat.com/2009/06/10/quote-of-the-week-9-negative-thermometers/#more-8362
http://www.climate-skeptic.com/2009/06/forgetting-about-physical-reality.html
Would appreciate some reference to a citation or an academician and/or a more in-depth answer than just "he or she is right" so that I can either get my opponent to understand where he is wrong, or understand it myself. Muchos gracias.
69.250.46.136 (
talk)
18:00, 19 June 2009 (UTC)
Hi. I'm halfway through working out the answer to a question and am now stuck. Here's what I have
"Let where n is a positive integer and . Find an expression for the largest root of the equation f(x)=0, distinguishing between the cases where n is even and n is odd. You may assume that ."
So after working through this I get solutions as follows:
provided
provided
provided
provided
where p is some integer.
First of all, is what I have correct? Secondly, how do you distinguish between odd and even? I can't see what difference it will make to my answer. Thanks asyndeton talk 20:51, 19 June 2009 (UTC)
Let u = 2nx. Then the function is
and this is 0 iff either sin u = 0 (so u is an integral multiple of π) or cos u = either 1 or −1/2 (so that u is an integral multiple of 2π/3).
The condition that x is between 0 and π/2 says that u is between 0 and nπ.
If n is even then the largest multiple of 2π/3 that is less than nπ is π(n − 2/3). If n is odd, then put "1/3" there instead of "2/3". (Just draw the picture on the x-axis with n going from 0 to about 5 or so, and you'll see it. Never mind what the curve looks like; just graph the zeros as I described them above.) Michael Hardy ( talk) 21:44, 19 June 2009 (UTC)