Hash join - Revision history

en>Rowena-san: Changed predicate to predicate

2014-09-19T14:34:03Z

Changed predicate to predicate

@@ Line 1: / Line 1: @@
-{{distinguish|Gelfond–Schneider constant}}
+== Louis Vuitton Pung  Vil nogen ==
-In [[mathematics]], '''Gelfond's constant''', named after [[Aleksandr Gelfond]], is ''e''<sup>{{pi}}</sup>, that is, ''[[e (mathematical constant)|e]]'' to the [[exponentiation|power]] of [[Pi|{{pi}}]]. Like both ''e'' and {{pi}}, this constant is a [[transcendental number]]. This was first established by Gelfond and may now be considered as an application of the [[Gelfond–Schneider theorem]], noting the fact that
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-:<math> e^\pi = (e^{i\pi})^{-i} = (-1)^{-i},</math>
+   <li>[http://www.histoirepassion.eu/spip.php?article1761/ http://www.histoirepassion.eu/spip.php?article1761/]</li>
-where ''i'' is the [[imaginary unit]].  Since &minus;''i'' is algebraic but not rational, ''e''<sup>{{pi}}</sup> is transcendental. The constant was mentioned in [[Hilbert's seventh problem]].<ref name=tijdeman>{{cite book | editor=Felix E. Browder | editor-link=Felix Browder | title=Mathematical Developments Arising from Hilbert Problems | series=[[Proceedings of Symposia in Pure Mathematics]] | volume=XXVIII.1 | year=1976 | publisher=[[American Mathematical Society]] | isbn=0-8218-1428-1 | first=Robert | last=Tijdeman | authorlink=Robert Tijdeman | chapter=On the Gel'fond–Baker method and its applications | pages=241–268 | zbl=0341.10026 }}</ref>  A related constant is <math>2^\sqrt{2}</math>, known as the [[Gelfond–Schneider constant]].  The related value {{pi}}&nbsp;+&nbsp;''e''<sup>{{pi}}</sup> is also irrational.<ref>{{cite journal|author=Nesterenko, Y|authorlink=Yuri Valentinovich Nesterenko|title=Modular Functions and Transcendence Problems|journal=[[Comptes rendus de l'Académie des sciences|Comptes Rendus de l'Académie des Sciences. Série I. Mathématique]]|volume=322|pages=909–914|year=1996|issue=10| zbl=0859.11047 }}</ref>
+   <li>[http://lt.luckv.com/forum.php?mod=viewthread&tid=1558692 http://lt.luckv.com/forum.php?mod=viewthread&tid=1558692]</li>
-==Numerical value==
+   <li>[http://www.shaffaf.net/spip.php?article929&lang=ar&id_forum=27372/ http://www.shaffaf.net/spip.php?article929&lang=ar&id_forum=27372/]</li>
-The decimal expansion of Gelfond's constant begins
+   <li>[http://www.tztea.com.cn/news/html/?255243.html http://www.tztea.com.cn/news/html/?255243.html]</li>
-:<math>e^\pi  \approx 23.14069263277926900572908636794854738\dots\,.</math>{{OEIS2C|id=A039661}}
-If one defines <math>\scriptstyle k_0\,=\,\tfrac{1}{\sqrt{2}}</math> and
+   <li>[http://www.hnyrlp.com/news/html/?58441.html http://www.hnyrlp.com/news/html/?58441.html]</li>
-:<math>k_{n+1}=\frac{1-\sqrt{1-k_n^2}}{1+\sqrt{1-k_n^2}}</math>
+ </ul>

en>Monkbot: /* Hybrid hash join */Fix CS1 deprecated date parameter errors

2014-01-20T18:26:11Z

Hybrid hash join: Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 20:26, 20 January 2014
Line 1:		Line 1:
	~~Luke Bryan can be a celebrity from~~ the ~~earning as well as job expansion initially second to his third restaurant record, And~~ , may be the ~~evidence. He broken on~~ the ~~[http~~://~~www~~.~~banburycrossonline~~.~~com jason aldean~~] ~~scene in 2005 along with his amusing mix of lower~~-~~residence ease of access, video legend fantastic seems~~ and ~~lines~~, is ~~placed t in a key way~~. The ~~new recor about the region chart~~ and #2 in the ~~take graphs~~, ~~producing it the 2nd maximum very first in those days of 2012 for any region musician~~. <br><br><br><br>The ~~son~~ of ~~your~~ , is ~~aware of perseverance~~ and ~~willpower are key elements in terms of an effective occupation~~- ~~. His first album, Keep Me, produced the most notable strikes “All My Girlfriends “Country~~ and ~~Say” Gentleman~~,~~” when his energy, Doin’ Issue, found~~ the ~~performer~~-~~a few right No~~. ~~4 singles~~: ~~In addition Getting in touch with Is a Fantastic Thing.”~~<br><br>~~During~~ the ~~slip~~ of ~~2011~~, ~~Concert tour: Luke Bryan & which had an outstanding selection of~~ , ~~which include~~ [http://~~lukebryantickets~~.~~neodga~~.com ~~meet and greet tickets~~] ~~Downtown.~~ [http://~~lukebryantickets~~.~~iczmpbangladesh~~.org luke bryan presale tickets] “It’s much like you’re obtaining a approval to go to the next level, says those artists that have been a part of the Concert tourmore than in a larger sized degree of designers.~~” It covered as one of the most successful~~ ~~trips in the 10-year background.<br><br>my web site;~~ [http://~~lukebryantickets~~.~~pyhgy~~.com ~~luke bryan on sale dates~~]		{{distinguish\|Gelfond–Schneider constant}}

			In [[mathematics]], '''Gelfond's constant''', named after [[Aleksandr Gelfond]], is ''e''<sup>{{pi}}</sup>, that is, ''[[e (mathematical constant)\|e]]'' to the [[exponentiation\|power]] of [[Pi\|{{pi}}]]. Like both ''e'' and {{pi}}, this constant is a [[transcendental number]]. This was first established by Gelfond and may now be considered as an application of the [[Gelfond–Schneider theorem]], noting the fact that

			:<math> e^\pi = (e^{i\pi})^{-i} = (-1)^{-i},</math>

			where ''i'' is the [[imaginary unit]]. Since −''i'' is algebraic but not rational, ''e''<sup>{{pi}}</sup> is transcendental. The constant was mentioned in [[Hilbert's seventh problem]].<ref name=tijdeman>{{cite book \| editor=Felix E. Browder \| editor-link=Felix Browder \| title=Mathematical Developments Arising from Hilbert Problems \| series=[[Proceedings of Symposia in Pure Mathematics]] \| volume=XXVIII.1 \| year=1976 \| publisher=[[American Mathematical Society]] \| isbn=0-8218-1428-1 \| first=Robert \| last=Tijdeman \| authorlink=Robert Tijdeman \| chapter=On the Gel'fond–Baker method and its applications \| pages=241–268 \| zbl=0341.10026 }}</ref> A related constant is <math>2^\sqrt{2}</math>, known as the [[Gelfond–Schneider constant]]. The related value {{pi}} + ''e''<sup>{{pi}}</sup> is also irrational.<ref>{{cite journal\|author=Nesterenko, Y\|authorlink=Yuri Valentinovich Nesterenko\|title=Modular Functions and Transcendence Problems\|journal=[[Comptes rendus de l'Académie des sciences\|Comptes Rendus de l'Académie des Sciences. Série I. Mathématique]]\|volume=322\|pages=909–914\|year=1996\|issue=10\| zbl=0859.11047 }}</ref>

			==Numerical value==
			The decimal expansion of Gelfond's constant begins

			:<math>e^\pi \approx 23.14069263277926900572908636794854738\dots\,.</math>{{OEIS2C\|id=A039661}}
			If one defines <math>\scriptstyle k_0\,=\,\tfrac{1}{\sqrt{2}}</math> and

			:<math>k_{n+1}=\frac{1-\sqrt{1-k_n^2}}{1+\sqrt{1-k_n^2}}</math>

			for <math>n > 0</math> then the sequence<ref>{{cite book\|author1-link=Jonathan Borwein \| last1=Borwein \| first1=J. \| last2=Bailey \| first2=D. \| title=Mathematics by Experiment: Plausible Reasoning in the 21st Century\|place=Wellesley, MA\|publisher=A K Peters\|year=2004\|page=137 \| isbn=1-56881-211-6 \| zbl=1083.00001 }}</ref>

			:<math>(4/k_{n+1})^{2^{-n}}</math>

			converges rapidly to <math>e^\pi</math>.

			==Geometric peculiarity==
			The volume of the ''n''-dimensional ball (or [[n-ball\|''n''-ball]]), is given by:

			:<math>V_n={\pi^\frac{n}{2}R^n\over\Gamma(\frac{n}{2} + 1)}.</math>

			where <math>R</math> is its radius and <math>\Gamma</math> is the [[gamma function]]. Any even-dimensional unit ball has volume:

			:<math>V_{2n}=\frac{\pi^n}{n!}\ </math>

			and, summing up all the unit-ball volumes of even-dimension gives:<ref>Connolly, Francis. University of Notre Dame{{full\|date=November 2012}}</ref>

			:<math>\sum_{n=0}^\infty V_{2n} = e^\pi. \,</math>

			== See also ==
			* [[Transcendental number]]
			* [[Transcendence theory]], the study of questions related to transcendental numbers
			* [[Euler's identity]]
			* [[Gelfond–Schneider constant]]

			==References==
			{{Reflist}}

			==Further reading==
			* [[Alan Baker (mathematician)\|Alan Baker]] and [[Gisbert Wüstholz]], ''Logarithmic Forms and Diophantine Geometry'', New Mathematical Monographs '''9''', Cambridge University Press, 2007, ISBN 978-0-521-88268-2

			==External links==
			* [http://mathworld.wolfram.com/GelfondsConstant.html Gelfond's constant at ''MathWorld'']
			* [http://web.archive.org/web/20091027100754/http://www.geocities.com/timeparadox/Muntekim.htm A new complex power tower identity for Gelfond's constant]
			* [http://mathworld.wolfram.com/AlmostInteger.html Almost Integer at ''MathWorld'']

			[[Category:Transcendental numbers]]
			[[Category:Mathematical constants]]

en>A3 nm: -useless caps

2012-07-10T18:47:48Z

-useless caps

New page

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