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	LEGGE (BILSON-LEGGE), HENRY - LoveToKnow Article on LEGGE (BILSON-LEGGE), HENRY (Site not responding. Last check: 2007-11-07)
		Legendre was also the author of a memoir upon triangles drawn upon a spheroid.
		Legendre's theorem is a fundamental one in geodesy, and his contributions to the subject are of the greatest importance.
		It will thus be seen that Legendre's works have placed him in the very foremost rank in the widely distinct subjects of elliptic functions, theory of numbers, attractions, and geodesy, and have given him a conspicuous position in connection with the integral calculus and other branches of mathematics.
	www.1911encyclopedia.org /L/LE/LEGGE_BILSON_LEGGE_HENRY.htm (2509 words)

	Legendre polynomials - Wikipedia, the free encyclopedia
		Note: The term Legendre polynomials is sometimes used (wrongly) to indicate the associated Legendre polynomials.
		The Legendre differential equation may be solved using the standard power series method.
		Legendre polynomials of fractional order exist and follow from insertion of fractional derivatives as defined by fractional calculus and non-integer factorials (defined by the gamma function) into the Rodrigues' formula.
	www.wikipedia.org /wiki/Legendre_polynomials (280 words)

	Adrien-Marie Legendre (Site not responding. Last check: 2007-11-07)
		At the age of 18, Legendre defended his thesis in mathematics and physics there but this was not quite as grand an achievement as it sounds to us today, for this consisted more of a plan of research rather than a completed thesis.
		Legendre became an associé in 1785, and then in 1787 he was a member of the team to make measurements of the Earth involving a triangulation survey between the Paris and Greenwich observatories.
		In 1791, Legendre became a member of the committee of the Académie des Sciences with the task to standardise weights and measures.
	www.stetson.edu /~efriedma/periodictable/html/Nd.html (564 words)

	Legendre
		In 1770, at the age of 18, Legendre defended his thesis in mathematics and physics at the Collège Mazarin but this was not quite as grand an achievement as it sounds to us today, for this consisted more of a plan of research rather than a completed thesis.
		Legendre's work replaced Euclid's "Elements" as a textbook in most of Europe and, in succeeding translations, in the United States and became the prototype of later geometry texts.
		Gauss was correct, but one could understand how hurtful Legendre must have found an attack on the rigour of his results by such a young man. Of course Gauss did not state that he was improving Legendre's result but rather claimed the result for himself since his was the first completely rigorous proof.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Legendre.html (1754 words)

	Adrian Marie Legendre (1752 - 1833)
		Legendre's analysis is of a high order of excellence, and is second only to that produced by Lagrange and Laplace, though it is not so original.
		Legendre's investigations had commenced with a paper written in 1786 on elliptic arcs, but here and in his other papers he treated the subject merely as a problem in the integral calculus, and did not see that it might be considered as a higher trigonometry, and so constitute a distinct branch of analysis.
		The superiority of their methods was at once recognized by Legendre, and almost the last act of his life was to recommend those discoveries which he knew would consign his own labours to comparative oblivion.
	www.maths.tcd.ie /pub/HistMath/People/Legendre/RouseBall/RB_Legendre.html (1138 words)

	Encyclopedia: Adrien-Marie Legendre (Site not responding. Last check: 2007-11-07)
		elliptic functions was built on Legendre's; some of Johann Carl Friedrich Gauss Johann Carl Friedrich Gauss (Gauß) (April 30, 1777 _ February 23, 1855) was a legendary German mathematician, astronomer and physicist with a very wide range of contributions; he is considered to be one of the greatest mathematicians of all time.
		Legendre transform, which is used to go from the Lagrangian to the Hamiltonian formulation of mechanics.
		The Legendre symbol is used by mathematicians in the area of number theory, particularly in the fields of factorization and quadratic residues.
	www.nationmaster.com /encyclopedia/Adrien_Marie-Legendre (1774 words)

	Legendre's Prime Number Conjecture (Site not responding. Last check: 2007-11-07)
		Most historical accounts of the Prime Number Theorem mention Legendre's experimental conjecture (made in 1798 and again in 1808) that x pi(x) = --------------- log(x) - A(x) where pi(x) is the number of primes less than x, and the limit of A(x) as x goes to infinity is 1.08366....
		Aside from the comment that Legendre's conjecture was based on "experimental evidence", I've never seen an explanation of how he actually arrived at the number 1.08366...
		The only other information I've found is in Tchebyshev's paper where he says Legendre "..begins by comparing his formula with the result of counting the primes in the most extended tables, namely those from 10,000 up to 1,000,000, after which he applies his formula to the solution of many problems".
	www.meta-religion.com /Mathematics/Biography/legendre.htm (360 words)

	Luc Legendre, Artist - The World and I Magazine
		Legendre's exhibition may have lacked the scandal of Duchamp's, but it was no less of an event for the painter.
		The result was a series of portraits of the people Legendre had seen on the street, somewhere between New York's Broadway and Los Angeles' Wilshire Boulevard: a honey-colored girl in a discotheque, two women dancing on a street corner, a homeless man squatting on a curb.
		Legendre, who is very much a student of the history of art and artists, feels a close kinship with those who have crossed over from Europe before him.
	www.worldandi.com /public/1991/june/ar12.cfm (1965 words)

	Legendre polynomials -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		Note: The term Legendre polynomials is sometimes used (wrongly) to indicate the (Click link for more info and facts about associated Legendre polynomials) associated Legendre polynomials.
		The Legendre differential equation may be solved using the standard (The sum of terms containing successively higher integral powers of a variable) power series method.
		The shifted Legendre polynomials are defined as being orthogonal on the unit interval [0,1]
	www.absoluteastronomy.com /encyclopedia/l/le/legendre_polynomials.htm (449 words)

	Legendre transformation - Wikipedia, the free encyclopedia
		The Legendre transformation is its own inverse, and is related to integration by parts.
		Legendre transformations are used in thermodynamics to transform between the different thermodynamic potentials, and in classical mechanics to derive Hamiltonian mechanics from Lagrangian mechanics, as well as the other way around.
		the Legendre conjugate of the pair (U, f) is defined to be the pair (V, g), where V is the image of U under the gradient mapping Df, and g is the function on V given by the formula
	en.wikipedia.org /wiki/Legendre_transformation (792 words)

	Fermat's Last Theorem: Adrien-Marie Legendre
		Legendre's reputation was made when he was able to win the Berlin Academy Prize in 1782.
		It is clear that Legendre was not happy with Gauss's words but in 1808, when Legendre came out with the next version of his textbook on number theory, he included Gauss's proof instead of his own.
		Legendre was fascinated by Euclid's parallel postulate and for many years attempted to provide a proof.
	fermatslasttheorem.blogspot.com /2005/10/adrien-marie-legendre.html (522 words)

	Geraldine Legendre \| JHU Cognitive Science Department
		Legendre, G. Morphological and Prosodic Alignment of Bulgarian Clitics.
		Legendre, G. & Rood, D. On the Interaction of Grammar Components in Lakhóta: Evidence from Split Intransitivity.
		Legendre, G. For an OT Conception of a Parallel Interface: Evidence from Basque V2.
	www.cog.jhu.edu /faculty/legendre (2925 words)

	Simeon E. LeGendre Jr. (Site not responding. Last check: 2007-11-07)
		LeGendre graduated from Lawrence High School in 1935 and from Boston College in 1939.
		LeGendre returned from the war in 1944 and married Alice R. Petteruti.
		Professor LeGendre and his wife Alice, the first president of the Ladies of Merrimack, very actively participated in the spiritual and social events of the college.
	www.eagletribune.com /news/stories/20020511/FN_002.htm (385 words)

	Search Results for Legendre
		Legendre submitted his results to the Academie des Sciences in Paris in January 1783 and these were highly praised by Laplace in his report delivered to the Academie in March.
		Legendre was sent a copy of the work and he sent it to Francois Francais although neither knew the identity of the author.
		Legendre was appointed one of the referees and he was able to prove case 2 thus completing the proof for n = 5.
	www-groups.dcs.st-and.ac.uk /~history/Search/historysearch.cgi?SUGGESTION=Legendre&CONTEXT=1 (4100 words)

	Legendre.htm
		His 1785 paper on number theory contains a number of important results such as the law of quadratic reciprocity for residues and the results that every arithmetic series with the first term coprime to the common difference contains an infinite number of primes.
		Legendre's major work on elliptic functions in Exercises du Calcul Intégral appeared in three volumes in 1811, 1817, and 1819.
		Legendre polynomials form an orthonormal basis for the vector space of polynomials.
	www.cse.ohio-state.edu /~brinkmei/math/Legendre.htm (136 words)

	Voltage Dependence of the Glycine Receptor-Channel Kinetics in the Zebrafish Hindbrain -- Legendre 82 (5): 2120 -- ...
		In the zebrafish hindbrain an increase in miniature IPSC (mIPSC) duration with membrane depolarization is correlated with
		Legendre, P. A reluctant gating mode of glycine receptor channels determines the time course of inhibitory miniature synaptic events in zebrafish hindbrain neurons.
		Legendre, P., and Korn, H. Voltage dependence of conductance changes evoked by glycine release in the zebrafish brain.
	jn.physiology.org /cgi/content/full/82/5/2120 (5808 words)

	Squares in Arithmetic Progression (mod p) (Site not responding. Last check: 2007-11-07)
		This is to be expected, because our Legendre symbols are unavoidable for ALL primes, so the only reason we do not have non-trivial progressions for p = 2, 3, 5, 7, or 11 is that in these cases the applicable common difference equals the prime itself.
		Our objective is to minimize the total number of Legendre symbols, and to include cases that involve both signs of these symbols, in order to maximize the coverage.
		The task is to find conditions, probably involving one or two more Legendre symbols, and progressions with step sizes of 13, 19, 29, 31, and 37 to complete the unavoidable set.
	www.mathpages.com /home/kmath291.htm (1063 words)

	Alexander's Gas & Oil Connections - Legendre oil fields on North West Shelf to be developed as stand alone project (Site not responding. Last check: 2007-11-07)
		Legendre oil fields on North West Shelf to be developed as stand alone project
		He said he Legendre South and Legendre North oil fields are expected to come on stream in 2001, with a target of peak production of 40,000 bpd.
		Appraisal and exploration drilling over the past 18 months together with the application of new technology has seen the Legendre South and Legendre North oil fields matured to the point where combined proved and probable reserves estimates have increased to 40.4 mm barrels of light crude oil.
	www.gasandoil.com /goc/company/cns92778.htm (218 words)

	Jacobi symbol -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		The Jacobi symbol is a generalization of the (Click link for more info and facts about Legendre symbol) Legendre symbol using the (Click link for more info and facts about prime factorization) prime factorization of the bottom number.
		The general statements about quadratic residuals with respect to the Legendre symbol cannot be made with the Jacobi symbol.
		Since the Jacobi symbol is a product of Legendre symbols, there are cases where two Legendre symbols evaluate to −1 and the Jacobi symbol evaluates to 1.
	www.absoluteastronomy.com /encyclopedia/J/Ja/Jacobi_symbol.htm (285 words)

	Simeon E. LeGendre Jr. (Site not responding. Last check: 2007-11-07)
		Simeon E. LeGendre Jr., 84, a longtime Andover resident, died Thursday, May 9 at the Melrose home of his daughter.
		LeGendre was an Andover resident for 58 years.
		His late wife, Alice R. LeGendre, was the first president of the Ladies of Merrimack and was very active with spiritual and social events there.
	www.andovertownsman.com /news/20020516/OB_001.html (336 words)

	Comic creator: Marc Legendre ('Ikke') (Site not responding. Last check: 2007-11-07)
		After completing his formal education, Marc Legendre became chief editor of Kuifje, the Dutch version of Tintin.
		Legendre became a versatile comics writer at the publishing house Standaard.
		Marc Legendre is also active in the worlds of advertising and the television.
	www.lambiek.net /legendre_m.htm (209 words)

	Cours particuliers / soutien scolaire / cours à domicile / cours particulier : Cours Legendre
		Partout en France, les Cours Legendre sont devenus la référence du soutien scolaire de qualité.
		Tout au long de l'année, les Cours Legendre vous proposent : des cours particuliers à domicile, des stages intensifs, des cours par correspondance, des cours d'été et de soutien scolaire, des cahiers de vacances, des séjours linguistiques.
		Les cours particuliers Legendre : des cours particuliers pour tous les niveaux et des cours particuliers dans toutes les matières.
	www.cours-legendre.fr (592 words)

	LAB #9: Legendre Polynomials
		The Legendre polyonomials are a basis for the set of polynomials, appropriate for use on the interval [-1,1].
		The Legendre polynomials form a basis for the linear space of polynomials.
		It will also be most convenient to have a "vector" version of the Legendre polynomial routine, that is, something that we can give a vector x of arguments to, and which will return the corresponding vector of values.
	www.csit.fsu.edu /~burkardt/math2070/lab_09.html (1352 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		An unusual feature of the FCNPAK subroutines for Legendre functions is the use of extended-range arithmetic, a software extension of ordinary floating-point arithmetic that greatly increases the exponent range of the representable numbers.
		In the case of the normalized Legendre polynomials, testing shows it to be about a factor of two.
		The names of the subroutines used for Legendre functions are XDLEGF XSLEGF XDNRMP XSNRMP where the LEGF subroutines compute the double and single precision associated Legendre functions and the NRMP subroutines compute the double and single precision normalized Legendre polynomials.
	www.umbc.edu /doc/cmlib/doc/fcnpak/Summary.html (600 words)

	Francis Legendre (Site not responding. Last check: 2007-11-07)
		METHUEN - Francis "Frank" Legendre, 86, of Methuen, died Sunday at Holy Family Hospital.
		Legendre loved both vegetable and flower gardening and saltwater fishing.
		He also enjoyed dancing and traveling with his wife, Evelyn (Gallant) Legendre, before she died in January.
	www.eagletribune.com /news/stories/19980304/OB_007.htm (135 words)

	Legendre, Adrien-Marie -- Encyclopædia Britannica (Site not responding. Last check: 2007-11-07)
		Little is known about Legendre's early life except that his family wealth allowed him to study physics and mathematics, beginning in 1770, at the Collège Mazarin (Collège des Quatre-Nations) in Paris and…
		Adrien-Marie Legendre was born in Toulouse, France, in 1752.
		He served as professor of mathematics at the École Militaire, Paris, from 1775 to 1780 and in 1795 became a professor at the École Normale.
	www.britannica.com /eb/article-9047635?tocId=9047635 (790 words)

	Legendre Polynomials (Site not responding. Last check: 2007-11-07)
		The weight function w(x) of the Legendre polynomials is unity, and this is what distinguishes them from the others and determines them.
		For finding solutions to Laplace's equation in spherical coordinates, the Legendre polynomials are sufficient so long as the problem is axially symmetric, in which there is no φ-dependence.
		The more general problem requires the introduction of related functions called the associated Legendre functions that are actually built up from Jacobi polynomials, and can also be expressed in terms of derivatives of the Legendre polynomials.
	www.du.edu /~jcalvert/math/legendre.htm (1164 words)

	A Modified Jacobi Sequence Construction Using Multi-Rate Legendre Sequences (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		Abstract: We propose a construction for length n = pq Modified Jacobi sequences using multi-rate length p and length q Legendre sequences, thereby reducing the LFSR complexity of Modified Jacobi sequence generation from O(pq) to O(p + q).
		4 Trace Representation of Legendre Sequences of Mersenne Prime..
		Legendre and Twin Prime Sequences: Trace and Multi-Rate..
	citeseer.ist.psu.edu /423519.html (278 words)

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