Pressure head - Revision history

en>Renn1988: /* Pressure Head Calculation */

2014-12-08T07:31:20Z

Pressure Head Calculation

← Older revision		Revision as of 09:31, 8 December 2014
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	~~In [[mathematics]]~~, ~~'''Cahen~~'s ~~constant''' is defined~~ as ~~an [[Series (mathematics)\|infinite series]] of [[unit fraction]]s, with alternating signs, derived from [[Sylvester's sequence]]:~~		Nice to satisfy you, I am Marvella Shryock. Since she was eighteen she's been working as a receptionist but her marketing by no means arrives. North Dakota is exactly where me and my spouse live. His wife doesn't like it the way he does but what he really likes doing is to do aerobics and he's been doing it for fairly a whilst.<br><br>Also visit my site :: [http://yenisehir.de/index.php?do=/profile-7188/info/ home std test kit]
	~~:<math>C = \sum\frac{(-1)^i}{s_i-1}=\frac11 - \frac12 + \frac16 - \frac1{42} + \frac1{1806} - \cdots\approx 0~~.~~64341054629~~.~~</math>~~
	~~By considering these fractions in pairs, we can also view Cahen~~'~~s constant as a series of positive unit fractions formed from~~ the ~~terms in even positions of Sylvester's sequence; this series for Cahen's constant forms its [[Greedy algorithm for Egyptian fractions\|greedy Egyptian expansion]]:~~
	~~:<math>C = \sum\frac{1}{s_{2i}}=\frac12+\frac17+\frac1{1807}+\frac1{10650056950807}+\cdots</math>~~
	~~This constant~~ is ~~named after Eugène Cahen (also known for the [[Cahen-Mellin integral]]), who first formulated~~ and ~~investigated its series {{harv\|Cahen\|1891}}.~~

	~~Cahen~~'s ~~constant is known to be [[Transcendental number\|transcendental]] {{harv\|Davison\|Shallit\|1991}}. It is notable as being one of~~ a ~~small number of naturally occurring transcendental numbers for which we know the complete [[continued fraction]] expansion: if we form the sequence~~
	~~:1, 1, 2, 3, 14, 129, 25298, 420984147, ..~~. ~~{{OEIS\|id=A006279}}~~
	~~defined by the [[recurrence relation]]~~
	:<~~math~~>~~q_{n+2} = q_n^2 q_{n+1} + q_n~~<~~/math~~>
	~~then the continued fraction expansion of Cahen's constant is~~
	:~~<math>~~[~~0,1,q_0^2,q_1^2,q_2^2,\ldots]</math>~~
	~~{{harv\|Davison\|Shallit\|1991}}.~~

	~~== References ==~~
	*{{citation
	~~\| last = Cahen \| first = Eugène~~
	~~\| title = Note sur un développement des quantités numériques, qui présente quelque analogie avec celui en fractions continues~~
	~~\| journal = Nouvelles Annales de Mathématiques~~
	~~\| volume = 10~~
	~~\| year = 1891~~
	~~\| pages = 508–514}}~~
	*{{citation
	~~\| last1 = Davison \| first1 = J. Les \| author2-link = Jeffrey Shallit \| last2 = Shallit \| first2 = Jeffrey O.~~
	~~\| title = Continued fractions for some alternating series~~
	~~\| journal = Monatshefte für Mathematik~~
	~~\| volume = 111~~
	~~\| year = 1991~~
	~~\| pages = 119–126~~
	~~\| doi = 10.1007/BF01332350~~
	~~\| issue = 2}}~~

	~~== External links ==~~
	*{{mathworld \| title = Cahen's Constant \| urlname = CahensConstant}}
	*{{citation \| title = The Cahen constant to 4000 digits \| url = http://pi.~~lacim.uqam.ca~~/~~piDATA/cahen~~.~~txt \| work~~ = ~~Plouffe's Inverter \| publisher = [[Université du Québec à Montréal]] \| accessdate= 2011~~-~~03-19}}~~

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

en>Uruiamme: This has been wrong for awhile. formula is valid for absolute, too

2013-12-10T06:20:49Z

This has been wrong for awhile. formula is valid for absolute, too

← Older revision		Revision as of 08:20, 10 December 2013
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	~~The writer~~ is ~~called Irwin~~. ~~Doing ceramics~~ is ~~what love doing~~. ~~Since she was 18 she~~'s ~~been working~~ as a ~~receptionist but her promotion never arrives~~. ~~Puerto Rico~~ is ~~where he and his wife live.~~<br><br>~~My web~~-~~site - [~~http://~~nuvem~~.tk/~~altergalactica~~/~~AliceedMaurermy nuvem~~.tk]		In [[mathematics]], '''Cahen's constant''' is defined as an [[Series (mathematics)\|infinite series]] of [[unit fraction]]s, with alternating signs, derived from [[Sylvester's sequence]]:
			:<math>C = \sum\frac{(-1)^i}{s_i-1}=\frac11 - \frac12 + \frac16 - \frac1{42} + \frac1{1806} - \cdots\approx 0.64341054629.</math>
			By considering these fractions in pairs, we can also view Cahen's constant as a series of positive unit fractions formed from the terms in even positions of Sylvester's sequence; this series for Cahen's constant forms its [[Greedy algorithm for Egyptian fractions\|greedy Egyptian expansion]]:
			:<math>C = \sum\frac{1}{s_{2i}}=\frac12+\frac17+\frac1{1807}+\frac1{10650056950807}+\cdots</math>
			This constant is named after Eugène Cahen (also known for the [[Cahen-Mellin integral]]), who first formulated and investigated its series {{harv\|Cahen\|1891}}.

			Cahen's constant is known to be [[Transcendental number\|transcendental]] {{harv\|Davison\|Shallit\|1991}}. It is notable as being one of a small number of naturally occurring transcendental numbers for which we know the complete [[continued fraction]] expansion: if we form the sequence
			:1, 1, 2, 3, 14, 129, 25298, 420984147, ... {{OEIS\|id=A006279}}
			defined by the [[recurrence relation]]
			:<math>q_{n+2} = q_n^2 q_{n+1} + q_n</math>
			then the continued fraction expansion of Cahen's constant is
			:<math>[0,1,q_0^2,q_1^2,q_2^2,\ldots]</math>
			{{harv\|Davison\|Shallit\|1991}}.

			== References ==
			*{{citation
			\| last = Cahen \| first = Eugène
			\| title = Note sur un développement des quantités numériques, qui présente quelque analogie avec celui en fractions continues
			\| journal = Nouvelles Annales de Mathématiques
			\| volume = 10
			\| year = 1891
			\| pages = 508–514}}
			*{{citation
			\| last1 = Davison \| first1 = J. Les \| author2-link = Jeffrey Shallit \| last2 = Shallit \| first2 = Jeffrey O.
			\| title = Continued fractions for some alternating series
			\| journal = Monatshefte für Mathematik
			\| volume = 111
			\| year = 1991
			\| pages = 119–126
			\| doi = 10.1007/BF01332350
			\| issue = 2}}

			== External links ==
			*{{mathworld \| title = Cahen's Constant \| urlname = CahensConstant}}
			*{{citation \| title = The Cahen constant to 4000 digits \| url = http://pi.lacim.uqam.ca/piDATA/cahen.txt \| work = Plouffe's Inverter \| publisher = [[Université du Québec à Montréal]] \| accessdate= 2011-03-19}}

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

145.53.180.22: /* Differential */

2012-07-20T13:11:41Z

Differential

New page

The writer is called Irwin. Doing ceramics is what love doing. Since she was 18 she's been working as a receptionist but her promotion never arrives. Puerto Rico is where he and his wife live.<br><br>My web-site - [http://nuvem.tk/altergalactica/AliceedMaurermy nuvem.tk]

← Older revision		Revision as of 09:31, 8 December 2014
Line 1:		Line 1:
	~~In [[mathematics]]~~, ~~'''Cahen~~'s ~~constant''' is defined~~ as ~~an [[Series (mathematics)\|infinite series]] of [[unit fraction]]s, with alternating signs, derived from [[Sylvester's sequence]]:~~		Nice to satisfy you, I am Marvella Shryock. Since she was eighteen she's been working as a receptionist but her marketing by no means arrives. North Dakota is exactly where me and my spouse live. His wife doesn't like it the way he does but what he really likes doing is to do aerobics and he's been doing it for fairly a whilst.<br><br>Also visit my site :: [http://yenisehir.de/index.php?do=/profile-7188/info/ home std test kit]
	~~:<math>C = \sum\frac{(-1)^i}{s_i-1}=\frac11 - \frac12 + \frac16 - \frac1{42} + \frac1{1806} - \cdots\approx 0~~.~~64341054629~~.~~</math>~~
	~~By considering these fractions in pairs, we can also view Cahen~~'~~s constant as a series of positive unit fractions formed from~~ the ~~terms in even positions of Sylvester's sequence; this series for Cahen's constant forms its [[Greedy algorithm for Egyptian fractions\|greedy Egyptian expansion]]:~~
	~~:<math>C = \sum\frac{1}{s_{2i}}=\frac12+\frac17+\frac1{1807}+\frac1{10650056950807}+\cdots</math>~~
	~~This constant~~ is ~~named after Eugène Cahen (also known for the [[Cahen-Mellin integral]]), who first formulated~~ and ~~investigated its series {{harv\|Cahen\|1891}}.~~

	~~Cahen~~'s ~~constant is known to be [[Transcendental number\|transcendental]] {{harv\|Davison\|Shallit\|1991}}. It is notable as being one of~~ a ~~small number of naturally occurring transcendental numbers for which we know the complete [[continued fraction]] expansion: if we form the sequence~~
	~~:1, 1, 2, 3, 14, 129, 25298, 420984147, ..~~. ~~{{OEIS\|id=A006279}}~~
	~~defined by the [[recurrence relation]]~~
	:<~~math~~>~~q_{n+2} = q_n^2 q_{n+1} + q_n~~<~~/math~~>
	~~then the continued fraction expansion of Cahen's constant is~~
	:~~<math>~~[~~0,1,q_0^2,q_1^2,q_2^2,\ldots]</math>~~
	~~{{harv\|Davison\|Shallit\|1991}}.~~

	~~== References ==~~
	*{{citation
	~~\| last = Cahen \| first = Eugène~~
	~~\| title = Note sur un développement des quantités numériques, qui présente quelque analogie avec celui en fractions continues~~
	~~\| journal = Nouvelles Annales de Mathématiques~~
	~~\| volume = 10~~
	~~\| year = 1891~~
	~~\| pages = 508–514}}~~
	*{{citation
	~~\| last1 = Davison \| first1 = J. Les \| author2-link = Jeffrey Shallit \| last2 = Shallit \| first2 = Jeffrey O.~~
	~~\| title = Continued fractions for some alternating series~~
	~~\| journal = Monatshefte für Mathematik~~
	~~\| volume = 111~~
	~~\| year = 1991~~
	~~\| pages = 119–126~~
	~~\| doi = 10.1007/BF01332350~~
	~~\| issue = 2}}~~

	~~== External links ==~~
	*{{mathworld \| title = Cahen's Constant \| urlname = CahensConstant}}
	*{{citation \| title = The Cahen constant to 4000 digits \| url = http://pi.~~lacim.uqam.ca~~/~~piDATA/cahen~~.~~txt \| work~~ = ~~Plouffe's Inverter \| publisher = [[Université du Québec à Montréal]] \| accessdate= 2011~~-~~03-19}}~~

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