Entire function - Revision history

DavidB4-bot: /* top */re-categorisation

2018-08-14T01:02:51Z

top: re-categorisation

DavidB4-bot: /* top */clean up & uniformity

2016-07-13T12:01:43Z

top: clean up & uniformity

Jpatt: Reverted edits by GiantWang (Talk) to last version by JacobB

2010-02-26T15:49:15Z

Reverted edits by GiantWang (Talk) to last version by JacobB

GiantWang at 15:47, February 26, 2010

2010-02-26T15:47:26Z

JacobB: additional copy editing (math tags formatiting - I may return to this to expand the article)

2009-07-15T01:43:10Z

additional copy editing (math tags formatiting - I may return to this to expand the article)

Aschlafly: copy edit; mathematicians are not always terrific spellers

2009-07-15T01:01:30Z

copy edit; mathematicians are not always terrific spellers

Pyfgcr: Added brief discussion of Liouville's theorem.

2009-01-18T23:12:20Z

Added brief discussion of Liouville's theorem.

Foxtrot: cat, grammar

2008-12-06T03:24:26Z

cat, grammar

NathanG: bold

2008-02-19T22:38:48Z

bold

Aschlafly: New page: An “entire” function in complex analysis is a function that is analytic on the whole complex plane. category:mathematics

2007-07-04T14:40:05Z

New page: An “entire” function in complex analysis is a function that is analytic on the whole complex plane. category:mathematics

New page

An “entire” function in [[complex analysis]] is a [[function]] that is [[analytic]] on the whole [[complex plane]].
[[category:mathematics]]

← Older revision		Revision as of 01:02, August 14, 2018
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	The main result governing the behavior of entire functions is Liouville's theorem, which states that a bounded entire function is constant. Here an entire function <math>f \ </math> is said to be bounded if there exists a constant <math>M \ </math> such that for all <math>z \in \mathbb{C} \ </math> the bound <math>f(z)<M \ </math> holds. Liouville's theorem yields a simple proof of the fundamental theorem of algebra: if <math>p(z) \ </math> were a polynomial with no roots in the complex plane, then one can prove that <math>1/p(z) \ </math> would be a bounded entire function, and thus constant.		The main result governing the behavior of entire functions is Liouville's theorem, which states that a bounded entire function is constant. Here an entire function <math>f \ </math> is said to be bounded if there exists a constant <math>M \ </math> such that for all <math>z \in \mathbb{C} \ </math> the bound <math>f(z)<M \ </math> holds. Liouville's theorem yields a simple proof of the fundamental theorem of algebra: if <math>p(z) \ </math> were a polynomial with no roots in the complex plane, then one can prove that <math>1/p(z) \ </math> would be a bounded entire function, and thus constant.
−	[[Category:Complex ~~analysis~~]]	+	[[Category:Complex Analysis]]

← Older revision		Revision as of 12:01, July 13, 2016
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	The main result governing the behavior of entire functions is Liouville's theorem, which states that a bounded entire function is constant. Here an entire function <math>f \ </math> is said to be bounded if there exists a constant <math>M \ </math> such that for all <math>z \in \mathbb{C} \ </math> the bound <math>f(z)<M \ </math> holds. Liouville's theorem yields a simple proof of the fundamental theorem of algebra: if <math>p(z) \ </math> were a polynomial with no roots in the complex plane, then one can prove that <math>1/p(z) \ </math> would be a bounded entire function, and thus constant.		The main result governing the behavior of entire functions is Liouville's theorem, which states that a bounded entire function is constant. Here an entire function <math>f \ </math> is said to be bounded if there exists a constant <math>M \ </math> such that for all <math>z \in \mathbb{C} \ </math> the bound <math>f(z)<M \ </math> holds. Liouville's theorem yields a simple proof of the fundamental theorem of algebra: if <math>p(z) \ </math> were a polynomial with no roots in the complex plane, then one can prove that <math>1/p(z) \ </math> would be a bounded entire function, and thus constant.
−	[[~~category~~:Complex analysis]]	+	[[Category:Complex analysis]]

← Older revision		Revision as of 15:49, February 26, 2010
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−	PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS	+	In [[complex analysis]], an '''entire function''' is a [[function]] that is [[analytic]] on the whole [[complex plane]].
		+
		+	The main result governing the behavior of entire functions is Liouville's theorem, which states that a bounded entire function is constant. Here an entire function <math>f \ </math> is said to be bounded if there exists a constant <math>M \ </math> such that for all <math>z \in \mathbb{C} \ </math> the bound <math>f(z)<M \ </math> holds. Liouville's theorem yields a simple proof of the fundamental theorem of algebra: if <math>p(z) \ </math> were a polynomial with no roots in the complex plane, then one can prove that <math>1/p(z) \ </math> would be a bounded entire function, and thus constant.
		+	[[category:Complex analysis]]

← Older revision		Revision as of 15:47, February 26, 2010
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−	~~In [[complex analysis]], an '''entire function''' is a [[function]] that is [[analytic]] on the whole [[complex plane]].~~	+	PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS PENIS
−
−	The main result governing the behavior of entire functions is Liouville's theorem, which states that a bounded entire function is constant. Here an entire function <math>f \ </math> is said to be bounded if there exists a constant <math>M \ </math> such that for all <math>z \in \mathbb{C} \ </math> the bound <math>f(z)<M \ </math> holds. Liouville's theorem yields a simple proof of the fundamental theorem of algebra: if <math>p(z) \ </math> were a polynomial with no roots in the complex plane, then one can prove that <math>1/p(z) \ </math> would be a bounded entire function, and thus constant.
−	~~[[category:Complex analysis]]~~

@@ Line 1: / Line 1: @@
 In [[complex analysis]], an '''entire function''' is a [[function]] that is [[analytic]] on the whole [[complex plane]].
-The main result governing the behavior of entire functions is Liouville's theorem, which states that a bounded entire function is constant.  Here an entire function <math>f</math> is said to be bounded if there exists a constant <math>M</math> such that for all <math>z \in \mathbb C</math> the bound <math>f(z)<M</math> holds.  Liouville's theorem yields a simple proof of the fundamental theorem of algebra: if <math>p(z)</math> were a polynomial with no roots in the complex plane, then one can prove that <math>1/p(z)</math> would be a bounded entire function, and thus constant.
+The main result governing the behavior of entire functions is Liouville's theorem, which states that a bounded entire function is constant.  Here an entire function <math>f \ </math> is said to be bounded if there exists a constant <math>M \ </math> such that for all <math>z \in \mathbb{C} \ </math> the bound <math>f(z)<M \ </math> holds.  Liouville's theorem yields a simple proof of the fundamental theorem of algebra: if <math>p(z) \ </math> were a polynomial with no roots in the complex plane, then one can prove that <math>1/p(z) \ </math> would be a bounded entire function, and thus constant.
 [[category:Complex analysis]]

← Older revision		Revision as of 01:01, July 15, 2009
Line 1:		Line 1:
	In [[complex analysis]], an '''entire function''' is a [[function]] that is [[analytic]] on the whole [[complex plane]].		In [[complex analysis]], an '''entire function''' is a [[function]] that is [[analytic]] on the whole [[complex plane]].
−	~~[[category:Complex analysis]].~~

−	The main result governing the behavior of entire functions is Liouville's theorem, which states that a bounded entire function is constant. Here an entire function <math>f</math> is said to be bounded if there exists a constant <math>M</math> such that for all <math>z \in \mathbb C</math> the bound <math>f(z)<M</math> holds. Liouville's theorem yields a simple proof of the fundamental theorem of ~~algabra~~: if <math>p(z)</math> were a polynomial with no roots in the complex plane, then one can prove that <math>1/p(z)</math> would be a bounded entire function, and thus constant.	+	The main result governing the behavior of entire functions is Liouville's theorem, which states that a bounded entire function is constant. Here an entire function <math>f</math> is said to be bounded if there exists a constant <math>M</math> such that for all <math>z \in \mathbb C</math> the bound <math>f(z)<M</math> holds. Liouville's theorem yields a simple proof of the fundamental theorem of algebra: if <math>p(z)</math> were a polynomial with no roots in the complex plane, then one can prove that <math>1/p(z)</math> would be a bounded entire function, and thus constant.
		+	[[category:Complex analysis]]

← Older revision		Revision as of 23:12, January 18, 2009
Line 1:		Line 1:
	In [[complex analysis]], an '''entire function''' is a [[function]] that is [[analytic]] on the whole [[complex plane]].		In [[complex analysis]], an '''entire function''' is a [[function]] that is [[analytic]] on the whole [[complex plane]].
−	[[category:Complex analysis]]	+	[[category:Complex analysis]].
		+
		+	The main result governing the behavior of entire functions is Liouville's theorem, which states that a bounded entire function is constant. Here an entire function <math>f</math> is said to be bounded if there exists a constant <math>M</math> such that for all <math>z \in \mathbb C</math> the bound <math>f(z)<M</math> holds. Liouville's theorem yields a simple proof of the fundamental theorem of algabra: if <math>p(z)</math> were a polynomial with no roots in the complex plane, then one can prove that <math>1/p(z)</math> would be a bounded entire function, and thus constant.

← Older revision		Revision as of 03:24, December 6, 2008
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−	An '''~~“entire”~~ function''' ~~in [[complex analysis]]~~ is a [[function]] that is [[analytic]] on the whole [[complex plane]].	+	In [[complex analysis]], an '''entire function''' is a [[function]] that is [[analytic]] on the whole [[complex plane]].
−	[[category:~~mathematics~~]]	+	[[category:Complex analysis]]

← Older revision		Revision as of 22:38, February 19, 2008
Line 1:		Line 1:
−	An “entire” function in [[complex analysis]] is a [[function]] that is [[analytic]] on the whole [[complex plane]].	+	An '''“entire” function''' in [[complex analysis]] is a [[function]] that is [[analytic]] on the whole [[complex plane]].
	[[category:mathematics]]		[[category:mathematics]]