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NewsTop StoriesFirst LookBy CategoryArchiveGossipThe HumThe Awful TruthWatch with KristinPlanet GossipH'wood Party GirlAsk the Answer B!MoreRed CarpetCool StuffPhotosPhotosThe Big PictureFashion PoliceTrend SpyParty PicsFaces in the NewsMoviesVideosGossipThe HumThe Awful TruthWatch with KristinPlanet GossipH'wood Party GirlAsk the Answer B!Lift Gamemystyle BlogRed CarpetSAGs 2008Golden Globes 2008Grammys 2008Emmys 2007Oscars 2007Grammys 2007SAGs 2007Golden Globes 2007MoviesReviewsThe Lyons DenReel GirlSundance 2008E!TunesMessage BoardsShowsThe 101Chelsea LatelyDaily 10Dr.Keeping Up withthe KardashiansKimoraLive from the Red CarpetThe Simple LifeSnoop Dogg's Father HoodThe SoupSunset TanYo on E!Live from the Red Carpet by Badgley Mischka Barbie DollAvailable now in our new Red Carpet Shop section!Will SAGs Be Daniel's Day?Can You Handle the Truth?Did We Just Meet the Winner?Stars in Orbit: Drew, Diane and L.What happens when a star dies during filming?Who cares about Sundance, anyway?Why do celebs in L.Strikewatch: What Does the DGA Deal Mean?Norbit Leads Oscar Pack with Eight Nominations!NewsTop StoriesFirst LookBy CategoryArchiveGossipThe HumThe Awful TruthWatch With KristinPlanet GossipH'wood Party GirlAsk the Answer BitchPhotosThe Big PictureFashion PoliceTrend SpyParty PicsFaces in the NewsMoviesFashionFashion PoliceTrend SpyCool StuffMoviesReviewsThe Lyons DenReel GirlCelebsCelebrity 101SightingsLookupE!ShowsAll ShowsSchedulePersonalitiesPlay a PartRed CarpetEmmys 2007Oscars 2007Grammys 2007Globes 2007MoreMessage BoardsShop E!NewsTop StoriesFirst LookBy CategoryArchiveGossipThe HumThe Awful TruthWatch with KristinPlanet GossipH'wood Party GirlAsk the Answer B!MoreRed CarpetCool StuffPhotosPhotosThe Big PictureFashion PoliceTrend SpyParty PicsFaces in the NewsMoviesVideosGossipThe HumThe Awful TruthWatch with KristinPlanet GossipH'wood Party GirlAsk the Answer B!Lift Gamemystyle BlogRed CarpetSAGs 2008Golden Globes 2008Grammys 2008Emmys 2007Oscars 2007Grammys 2007SAGs 2007Golden Globes 2007MoviesReviewsThe Lyons DenReel GirlSundance 2008E!TunesMessage BoardsShowsThe 101Chelsea LatelyDaily 10Dr.Keeping Up withthe KardashiansKimoraLive from the Red CarpetThe Simple LifeSnoop Dogg's Father HoodThe SoupSunset TanYo on E!Live from the Red Carpet by Badgley Mischka Barbie DollAvailable now in our new Red Carpet Shop section!Will SAGs Be Daniel's Day?Can You Handle the Truth?Did We Just Meet the Winner?Stars in Orbit: Drew, Diane and L.What happens when a star dies during filming?Who cares about Sundance, anyway?Why do celebs in L.Strikewatch: What Does the DGA Deal Mean?Norbit Leads Oscar Pack with Eight Nominations!NewsTop StoriesFirst LookBy CategoryArchiveGossipThe HumThe Awful TruthWatch With KristinPlanet GossipH'wood Party GirlAsk the Answer BitchPhotosThe Big PictureFashion PoliceTrend SpyParty PicsFaces in the NewsMoviesFashionFashion PoliceTrend SpyCool StuffMoviesReviewsThe Lyons DenReel GirlCelebsCelebrity 101SightingsLookupE!ShowsAll ShowsSchedulePersonalitiesPlay a PartRed CarpetEmmys 2007Oscars 2007Grammys 2007Globes 2007MoreMessage BoardsShop E!This article or section is in need of attention from an expert on the subject.Please help recruit one or improve this article yourself.See the talk page for details.This article or section may contain original research or unverified claims.Please improve the article by adding references.See the talk page for details.This article needs additional citations for verification.Please help improve this article by adding reliable references.This article is about the American entertainment television channel and some of its international variants.For its Canadian equivalent, see E!Entertainment Television is an American cable television and direct broadcast satellite network.From November 2006 onwards, it became wholly owned by Comcast.About the network
2 Personalities
3 Michael Jackson trial
4 Criticism
5 Original programming
5.Early Movietime hosts included Greg Kinnear, Paula Abdul, Katie Wagner, and Richard Blade.Three years later, in June 1990, Movie Time was renamed E!Hollywood news and gossip, and fashion.In November 2006, Comcast bought the Walt Disney Company's 39.Canada as of September 2007.Israel and throughout Latin America.In Canada a similar channel, Star!In September 2007, the E!CH, as a Canadian version of E!American channel's entertainment programming with primetime programming mainly acquired from the major U.The network has the unusual distinction of showing the technical end credits at the beginning of the program in order to seamlessly transition between shows without losing viewers (most other cable channels and even broadcast networks do this nowadays), meaning there is no commercial break between two shows.Another unusual distinction is that some sponsor tags credit current Broadway shows running in New York City, obviously and subliminally meant only for those viewers.In the Philippines, the network has delayed telecast from the selected programs in U.Lifestyle Network and ETC Entertainment Central.Personalities
Award shows and the red carpet events, premieres and E!News have been hosted and are scheduled to have host Heidieh Croce the late Jim Croce's daughter and by a variety of personalities.DePandi) host award shows and E!Veitch) hosts all season premieres and events for television programming along with her online column Watch With Kristin.Marc Malkin provides breaking news and commentary on E!News and various other programs on the network along with his online column "Planet Gossip" and online videoblog of the same name.Previous hosts include Michael Castner on Inside Word, Behind the Scenes, Live From the Red Carpet and Sex On the Riviera, Brooke Burke on Wild On!Rank, Jules Asner on Revealed with Jules Asner and Alisha Davis with John Burke on E!Red carpet events, now called Live From the Red Carpet, have been hosted previously by Joan Rivers (often with daughter Melissa Rivers), Star Jones, Kathy Griffin, and Nicky Hilton.Other hosts have included Emme on Fashion Emergency, Suzanne Sena on Celebrity Homes (now with Kristin Malia) and A.Benza on Mysteries and Scandals.Palms and The Anna Nicole Show respectively.Michael Jackson's 2005 trial and acquittal.As no cameras were allowed in the courtroom, E!The nightly airings of these reenactments attracted high ratings (for a basic cable channel).Simpson civil trial, and covered the earlier criminal trial live.Criticism
During the week of Dimebag Darrell Abbott's birthday E!Channel producers contacted Pantera publicist Jane Hoffman to license the video tape of Dimebag's murder and to have permission to reenact it for a show titled 20 Most Horrifying Hollywood Murders.In a letter made public, Hoffman among turning down the request wrote, "I realize there is nothing anyone can do to stop E!The letter closes with:
I ask that you all please take a moment from your busy days and close your eyes.Live out the fantasy of playing your favorite instrument onstage.Your closest friends in the world surround you, either in the band or in your crew.From one side of the stage, a man approaches.Thinking he's a security guy or a drunk fan who's just a bit out a line, you continue to perform.Two seconds later, he lifts his arms, aims a rifle at your brother, your best friend, your buddy and blows his brains out, not three feet from where you are.Now imagine it's a few years later and you turn on the TV set.Just in case you may be having at least a five minute respite from that scene that plays over and over in your head, just in case .....Only with some two bit actor who thinks this is his big Hollywood break.True Hollywood Story
The Soup
Daily 10
Fashion Police
The Girls Next Door (international title: Girls of the Playboy Mansion)
Dr.Chelsea Lately
Child Star Confidential
House of Carters
Love Ride
Movies We Love
Starveillance
Sunset Tan
Boulevard of Broken Dreams
Paradise City
Tales from the Hoff
Keeping Up With The Kardashians
Snoop Dogg's Father Hood
Additionally, it has an evening news broadcast, E!The channel also broadcasts classic episodes of Saturday Night Live (Not aired outside the United States).The network also simulcasts Bloomberg TV in the early morning hours, and airs Totally Outrageous Behavior, a show shared with sister channel G4.Single
The Anna Nicole Show
The Gossip Show
Mysteries and Scandals
Howard Stern
Love Is in the Heir
The Gastineau Girls
My Crazy Life
The Entertainer starring Wayne Newton
It's Good to Be...Celebrities Uncensored
Star Dates
Love Chain
Revealed with Jules Asner
Talk Soup (however The Soup is a reworked version of this show)
Night Stand
Taradise
Wild On!Online content
Leslie Gornstein (Answer B!External links
Wikinews: David Shankbone interviews Michael Musto about the art of celebrity journalism
E!Online International Official Site
E!UK TV Listings and Schedules
E!Latin America Official Site (In Spanish)
E!Career Opportunities listed on EntertainmentCareers.This page was last modified 20:59, 14 January 2008.All text is available under the terms of the GNU Free Documentation License.For comparison, functions 2x (dotted curve) and 4x (dashed curve) are shown; they are not tangent to the line of slope 1 (red).The function ex so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base e.It has a number of equivalent definitions; some of them are given below.The number e is occasionally called Euler's number after the Swiss mathematician Leonhard Euler, or Napier's constant in honor of the Scottish mathematician John Napier who introduced logarithms.Mascheroni constant, sometimes called simply Euler's constant.Since e is transcendental, and therefore irrational, its value cannot be given exactly as a finite or eventually repeating decimal.The numerical value of e truncated to 20 decimal places is:
2.Stochastic representations of e
5.History
The first references to the constant were published in 1618 in the table of an appendix of a work on logarithms by John Napier.However, this did not contain the constant itself, but simply a list of natural logarithms calculated from the constant.It is assumed that the table was written by William Oughtred.The first known use of the constant, represented by the letter b, was in correspondence from Gottfried Leibniz to Christiaan Huygens in 1690 and 1691.Leonhard Euler started to use the letter e for the constant in 1727, and the first use of e in a publication was Euler's Mechanica (1736).While in the subsequent years some researchers used the letter c, e was more common and eventually became the standard.The exact reasons for the use of the letter e are unknown, but it may be because it is the first letter of the word exponential.Another possibility is that Euler used it because it was the first vowel after a, which he was already using for another number, but his reason for using vowels is unknown.It is unlikely that Euler chose the letter because it is the first letter of his surname, since he was a very modest man and tried to give proper credit to the work of others.Jacob Bernoulli discovered this constant by studying a question about compound interest.Bernoulli noticed that this sequence approaches a limit for more and smaller compounding intervals.R) dollars at simple interest, will yield eR dollars with continuous compounding.Bernoulli trials
The number e itself also has applications to probability theory, where it arises in a way not obviously related to exponential growth.Suppose that a gambler plays a slot machine with a one in n probability and plays it n times.This is an example of a Bernoulli trials process.Each time the gambler plays the slots, there is a one in one million chance of winning.Playing one million times is modelled by the binomial distribution, which is closely related to the binomial theorem.Derangements
Another application of e, also discovered in part by Jacob Bernoulli along with Pierre Raymond de Montmort is in the problem of derangements, also known as the hat check problem.Here n guests are invited to a party, and at the door each guest checks his hat with the butler who then places them into labelled boxes.But the butler does not know the name of the guests, and so must put them into boxes selected at random.The problem of de Montmort is: what is the probability that none of the hats gets put into the right box.Furthermore, the number of ways the hats can be placed into the boxes so that none of the hats is in the right box is exactly n!Asymptotics
The number e occurs naturally in connection with many problems involving asymptotics.The principal motivation for introducing the number e, particularly in calculus, is to perform differential and integral calculus with exponential functions and logarithms.Consequently, the exponential function with base e is particularly suited to doing calculus.Choosing e, as opposed to some other number, as the base of the exponential function makes calculations involving the derivative much simpler.Once again, there is an undetermined limit which depends only on the base a, and if that base is e, the limit is one.The logarithm in this special base is called the natural logarithm (often represented as "ln"), and it also behaves well under differentiation since there is no undetermined limit to carry through the calculations.One way is to set the derivative of the exponential function ax to ax.In each case, one arrives at a convenient choice of base for doing calculus.In fact, these two bases are actually the same, the number e.Alternative characterizations
See also: Representations of e
Other characterizations of e are also possible: one is as the limit of a sequence, another is as the sum of an infinite series, and still others rely on integral calculus.So far, the following two (equivalent) properties have been introduced:
1.The following three characterizations can be proven equivalent:
3.It was the first number to be proved transcendental without having been specifically constructed for this purpose (compare with Liouville number).The proof was given by Charles Hermite in 1873.It is conjectured to be normal.The number e can be represented as a real number in a variety of ways: as an infinite series, an infinite product, a continued fraction, or a limit of a sequence.Still other less common representations are also available.Many other series, sequence, continued fraction, and infinite product representations of e have also been developed.Stochastic representations of e
In addition to the deterministic analytical expressions for representation of e, as described above, there are some stochastic protocols for estimation of e.In one such protocol, random samples X1,X2,...Xn of size n from the uniform distribution on (0, 1) are used to approximate e.Thus sample averages of U variables will approximate e.Known digits
The number of known digits of e has increased dramatically during the last decades.This is due both to the increase of performance of computers as well as to algorithmic improvements.In contemporary internet culture, individuals and organizations frequently pay homage to the number e.Silicon Valley, and later in Cambridge, Massachusetts; Seattle, Washington; and Austin, Texas.Solving this problem and visiting the advertised web site led to an even more difficult problem to solve, which in turn leads to Google Labs where the visitor is invited to submit a resume.In another instance, the eminent computer scientist Donald Knuth let the version numbers of his program METAFONT approach e.The versions are 2, 2.An Introduction to the History of Mathematics.Introduction to probability theory (published online under the GFDL), p.See, for instance, Kline, M.Calculus: An intuitive and physical approach, Dover, section 12."The Derived Functions of Logarithmic Functions."This is the approach taken by Klein (1998).Estimating the Value of e by Simulation The American Statistician, Vol.Activities (retrieved December 26, 2007).New Scientist 21st July 2007 p.Searchers with Math Puzzle", NPR."The story of e", by Robin Wilson at Gresham College, 28 February 2007 (available for audio and video download)
Class Library for Numbers (part of the GiNaC distribution) includes example code for computing e to arbitrary precision.Estimate Experiment) for computing e using a simulation based on uniform distribution.This page was last modified 20:01, 24 January 2008.All text is available under the terms of the GNU Free Documentation License.Forgot your User ID or Password?An important message to E*TRADE Customers.PLEASE READ THE IMPORTANT DISCLOSURES BELOW.Banking and lending products and services are offered by E*TRADE Bank, a Federal savings bank, Member FDIC, or its subsidiaries.E*TRADE Securities LLC and E*TRADE Bank are separate but affiliated companies.System response and account access times may vary due to a variety of factors, including trading volumes, market conditions, system performance, and other factors.The constant is base of the
natural logarithm.Bailey 1988,
Borwein et al.Sloane's A007676
and A007677),
which are good to 0, 0, 1, 1, 2, 3, 3, 4, 5, 5, ...Engel
expansion, namely 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, ...Guillera and Sondow 2005, Sondow 2005).Borwein and Bailey 2003, p.He repeats: I shouldn't be tippling, I shouldn't be toppling here!In showing a painting to probably a critical or venomous lady, anger dominates.We present a mnemonic to memorize a constant so exciting that Euler exclaimed: '!Taylor series, an easy summation formula, obvious, clear,
elegant!These end at positions 21, 372, 8092, 102128, 1061613, 12108841, ...The Number e: The Base of Natural Logarithms.Mathematics by Experiment: Plausible Reasoning in the 21st Century.Wellesley, MA: A K Peters, 2003.Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi.Form Approximations to the Logarithmic
Constant e.Cambridge, England: Cambridge University
Press, pp.Problem of the Month (August 2004).The Scientific American Book of Mathematical Puzzles and Diversions.New York: Simon and Schuster, pp.The
Unexpected Hanging and Other Mathematical Diversions.Chicago, IL: Chicago
University Press, pp.The Story of a Number.Princeton, NJ: Princeton University
Press, 1994.Irrationality of the numbers e and .The Mathematical Papers of Isaac Newton, Vol.New York: Cambridge University Press, 1968.New York: Random House, 1963.The Simple Continued Fraction Expression of e.Table of Current Records for the Computation of Constants.Spigot Algorithm for the Digits of .In From Zero to Infinity, 4th ed.Line Encyclopedia of Integer Sequences.Geometric Proof that Is Irrational and
a New Measure of Its Irrationality.Liouville Normal Numbers from Rational Functions.The Penguin Dictionary of Curious and Interesting Numbers.Middlesex, England: Penguin Books, p.July 9, 2007
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