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	Mathematical Table - LoveToKnow 1911
		The latter, which was extracted from the Tables du cadastre, is a continuation of a table in W. Gardiner's Tables of Logarithms (London, 1742; reprinted at Avignon; 1770), which gives logarithms of all numbers to moo, and of uneven numbers from woo to 1143.
		Values of f x ex2 dx and e x2 f x e xl dx.-These functions are em ployed in researches connected with n refractios, theory of errors, conduction of heat, andc.
		Bessel, Fundamenta astronomiae (Konigsberg, 1818), has log i o (e x2 erfc x) from x =o to I at intervals of oi to 7 places, likewise for argument log i o x, the arguments increasing from o to at intervals of oi.
	www.1911encyclopedia.org /Mathematical_Table (16773 words)

	Friedrich Bessel - Wikipedia, the free encyclopedia
		Bessel was the son of a civil servant, and at the age of 14 he was apprenticed to the import-export concern Kulenkamp.
		With this work under his belt, Bessel was able to achieve the feat for which he is best remembered today: he is credited with being the first to use parallax in calculating the distance to a star.
		In 1838 Bessel won the "race", announcing that 61 Cygni had a parallax of 0.314 arcseconds; which, given the diameter of the Earth's orbit, indicated that the star was ~3 parsecs away.
	en.wikipedia.org /wiki/Friedrich_Wilhelm_Bessel (562 words)

	Friedrich Wilhelm Bessel - Wikipedia
		Bessel era figlio di un funzionario pubblico, all'età di 14 anni lavorò come apprendista in una ditta di import-export.
		Nel 1838 Bessel calcolò che 61 Cygni aveva una parallasse di 0.314 secondi d'arco; che, dato il diametro dell'orbita della Terra, indicava che la stella era lontana circa 3 parsec (il satellite Hipparcos ha calcolato la parallasse a 0.28547 secondi d'arco).
		Bessel batté in velocità Friedrich Georg Wilhelm Struve e Thomas Henderson che nello stesso anno misurarono la parallasse di Vega e Alpha Centauri.
	it.wikipedia.org /wiki/Friedrich_Wilhelm_Bessel (450 words)

	Friedrich Wilhelm Bessel - Wikipedia
		Dieser Artikel behandelt den deutsche Wissenschaftler Friedrich Wilhelm Bessel.
		Bessel besuchte das Gymnasium in Minden bis zur Untertertia.
		Bessel stieß beim aufgeschlossenen Olbers auf Interesse und gewann in ihm einen großen Mentor.
	de.wikipedia.org /wiki/Friedrich_Wilhelm_Bessel (979 words)

	NationMaster - Encyclopedia: Friedrich Bessel (Site not responding. Last check: 2007-10-15)
		Friedrich Wilhelm Bessel (July 22, 1784 – March 17, 1846) was a German mathematician, astronomer, and systematizer of the Bessel functions (which, despite their name, were discovered by Daniel Bernoulli).
		Friedrich Wilhelm Bessel (July 22, 1784 - March 17, 1846) was a German mathematician, astronomer, and discoverer of the Bessel functions.
		Bessel's greatest astronomical achievement was the first successful use of parallax to determine the distance to a star.
	www.nationmaster.com /encyclopedia/Friedrich-Bessel (1611 words)

	Bessel function - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-15)
		Bessel's equation arises when finding separable solutions to Laplace's equation and the Helmholtz equation in cylindrical or spherical coordinates, and Bessel functions are therefore especially important for many problems of wave propagation, static potentials, and so on.
		Bessel functions also have useful properties for other problems, such as signal processing (e.g., see FM synthesis, Kaiser window, or Bessel filter).
		This is the approach that Bessel used, and from this definition he derived several properties of the function.
	www.sciencedaily.com /encyclopedia/bessel_function (1510 words)

	Bessel, Friedrich Wilhelm (1784-1846)
		Bessel was a superb observer and made many important contributions to positional astronomy, including, in 1838, the first direct measurement of a star's distance, that of 61 Cygni, by trigonometric parallax.
		Much of Bessel's work dealt with perturbations (wobbles) in the motion of planets and stars caused by the gravitational influence of other bodies.
		Bessel argued against the existence of life on the Moon at a time when several notable compatriots of his, including Gauss, Gruithuisen, Littrow, and Olbers, were in the pro-selenite camp.
	www.daviddarling.info /encyclopedia/B/Bessel.html (397 words)

	Bessel function (Site not responding. Last check: 2007-10-15)
		The graphs of Bessel functions look roughly like oscillating sine or cosine functions that decay proportional to 1/√ x (see also their asymptotic forms, below), although their roots are not generally periodic except asymptotically for large x.
		The Bessel functions are valid even for complex arguments x, and an important special case is that of a purely imaginary argument.
		In fact, there are simple closed-form expressions for the Bessel functions of half-integer order in terms of the standard trigonometric functions, and therefore for the spherical Bessel functions.
	www.serebella.com /encyclopedia/article-Bessel_function.html (1087 words)

	A Bessel Filter Crossover, and Its Relation to Others
		The Bessel filter uses a p(s) which is a Bessel polynomial, but the filter is more properly called a Thomson filter, after one of its developers [7].
		Bessel low-pass filters have maximally flat group delay about 0 Hz [9], so the phase response is approximately linear in the passband, while at higher frequencies the linearity degrades, and the group delay drops to zero (see Fig.
		Bessel polynomials of degree three or higher are not inherently symmetric, but may be normalized to be nearly symmetric by requiring a phase shift at the design frequency of 45 degrees per order, negative for the low-pass, positive for the high-pass.
	www.rane.com /note147.html (2874 words)

	Bessel (crater) - Wikipedia, the free encyclopedia
		Bessel is a small lunar crater that is located in the southern half of the Mare Serenitatis.
		Bessel is not of sufficient size to have developed the terrace structures of larger craters.
		A large ray, most likely from Tycho crater, crosses the mare from north to south, passing by Bessel crater along the western side.
	en.wikipedia.org /wiki/Bessel_(crater) (217 words)

	Bessel function - LoveToKnow 1911 (Site not responding. Last check: 2007-10-15)
		These functions are named after Friedrich Wilhelm Bessel, who in 1817 introduced them in an investigation on Kepler's Problem.
		Although Bessel was the first to systematically treat of these functions, it is to be noted that in 1732 Daniel Bernoulli obtained the function of zero order as a solution to the problem of the oscillations of a chain suspended at one end.
		The remarkable connexion between Bessel's functions and spherical harmonics was established in 1868 by F. Mehler, who proved that a simple relation existed between the function of zero order and the zonal harmonic of order n.
	81.1911encyclopedia.org /B/BE/BESSEL_FUNCTION.htm (396 words)

	Friedrich Wilhelm Bessel (Site not responding. Last check: 2007-10-15)
		Bessel's work had now become known internationally, and he was honored with the award of the Lalande Prize from the Institut de France for his tables of refraction based on Bradley's observations.
		Bessel also had a very significant impact on university teaching despite the fact that he never had a university education.
		Bessel, Jacobi, and Neumann are intimately linked to the reform of teaching at universities, first in Germany and then throughout the world.
	www.stetson.edu /~efriedma/periodictable/html/Bk.html (648 words)

	Bessel, Friedrich Wilhelm - Hutchinson encyclopedia article about Bessel, Friedrich Wilhelm
		He was the first person to find the approximate distance to a star by direct methods when he measured the parallax (annual displacement) of the star 61 Cygni in 1838.
		Bessel's work laid the foundations for a more accurate calculation of the scale of the universe and the sizes of stars, galaxies, and clusters of galaxies.
		This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.
	encyclopedia.farlex.com /Bessel,%20Friedrich%20Wilhelm (358 words)

	Bessel's Comet Candidate of November 9, 1808 (Site not responding. Last check: 2007-10-15)
		24-year old Friedrich Wilhelm Bessel was looking for the comet observed in March 1808, that Olbers and he had calculated to have brightened again, to provide hope for a rediscovery in the evening sky.
		On November 7, 1808, Bessel perceived two objects that appeared nebulous at first sight, one of which turned out to be a simple star in clearer air.
		Bessel was quite certain to have seen something on November 9 which was no more present later, but equally that it had not been the comet he originally had looked for, as this should have been visible in other evenings also.
	www.seds.org /~spider/spider/Misc/bessel_c1808.html (342 words)

	Bessel function (Site not responding. Last check: 2007-10-15)
		Bessel functions first defined by the Swiss mathematician Daniel Bernoulli and named after Friedrich Bessel are canonical solutions y (x) of Bessel's differential equation :
		Bessel's equation arises when finding separable solutions Laplace's equation and the Helmholtz equation in cylindrical or spherical coordinates and Bessel functions are therefore important for many problems of wave propagation potentials and so on.
		The graphs of Bessel functions look roughly oscillating sine or cosine functions that decay to 1/√ x (see also their asymptotic forms below) their roots are not generally periodic except for large x.
	www.freeglossary.com /Bessel_differential_equation (1119 words)

	amtage.de - das Minden-Magazin - Friedrich-Wilhelm Bessel
		Friedrich Wilhelm Bessel (1784-1846) ist diese Frage verhältnismäßig genau beantwortet.
		Bessel, der gerade erst 20-jährige Kaufmann, berechnet in seiner Freizeit dessen Bahn aus einer Reihe von vorliegenden Messdaten.
		31 Jahre später - Bessel ist längst ein anerkannter Astronom - kann er den wiederkehrenden Kometen in seiner eigenen Sternwarte in Königsberg beobachten.
	www.amtage.de /minden/Bessel_und_Minden/bessel_und_minden.html (1089 words)

	James Bradley Summary
		Bessel's catalog in 1818, with 3,000 star positions, was largely based on Bradley's observations.
		The publication of his observations was delayed by disputes about their ownership; but they were finally issued by the Clarendon Press, Oxford, in two folio volumes (1798, 1805).
		The insight and industry of Friedrich Wilhelm Bessel were, however, needed for the development of their fundamental importance.
	www.bookrags.com /James_Bradley (1530 words)

	Bessel function (Site not responding. Last check: 2007-10-15)
		Bessel's equation arises when finding separable solutions to Laplace's equation and the Helmholtz equation in cylindrical or spherical coordinates, and Bessel functions are therefore especially important for many problems of wave propagation, static potentials,and so on.
		The Bessel functions are valid even for complex argumentsx, and an important special case is that of a purely imaginary argument.
		In fact, there are simple closed-form expressions for the Bessel functions of half-integer order in terms of the standard trigonometric functions, and therefore for thespherical Bessel functions.
	www.therfcc.org /bessel-function-143035.html (907 words)

	Bessel-Ellipsoid - Bedeutung, Definition, Erklärung im netlexikon
		Das Bessel-Ellipsoid (auch Bessel 1841) ist ein wichtiges Referenzellipsoid für Europa.
		Es wurde 1841 von Friedrich Wilhelm Bessel aus den Daten großräumiger Vermessungen in Europa (auch Russland) und in Indien abgeleitet.
		Nach der Veröffentlichung Bessels anno 1841 war "sein" Ellipsoid das bei weitem modernste und wurde in den nächsten Jahrzehnten praktisch allen neueren Vermessungsnetzen zugrunde gelegt.
	www.lexikon-definition.de /Bessel-Ellipsoid.html (372 words)

	★ Reviews for Bessel,_Richard
		As Richard Bessel notes in his introduction, the Third Reich is not just the story of good versus evil but is a more complex study characterized by contradictions and paradoxes.
		Bessel's essay is entitled "Political Violence and the Nazi Seizure of Power." Bessel looks at the violence that helped the Nazi party gain power, which was often seen as legitimate when working as an "auxiliary police" force, and the violence against Jews, which was seen as excessive and hindered Nazi support.
		Resentment, claims Bessel, was also present in the cultural-economic sphere where it was felt that introducing women and children into the workforce had sowed the seeds of moral decline.
	authors.booksunderreview.com /B/Bessel,_Richard (945 words)

	Highbeam Encyclopedia - Search Results for Bessel,
		Bessel, Friedrich Wilhelm (1784–1846) German astronomer and mathematician.
		Bessel devised a system for analysing and reducing astronomical observations, made the first accepted measurements of the distance of a star (61 Cygni), and accurately predicted that Sirius and Procyon are binary...
		He became director of the observatory at the Univ. of Bonn in 1837 and continued there the work of determining the positions of stars that F. Bessel had begun at Königsberg.
	www.encyclopedia.com /SearchResults.aspx?Q=Bessel, (740 words)

	Imago Mundi - Friedrich Bessel.
		Bessel, Friedrich Wilhelm (23 juillet 1784 - 17 mars 1846) - Né à Minden, en Westphalie, quitta le commerce en 1805 pour entrer comme assistant à l'observatoire de Lilienthal, près de Brême, et s'y livrer aux études astronomiques sous la direction de Schröter, à qui Olbers l'avait recommandé.
		Bessel a introduit en 1823 la correction de l'erreur personnelle, dite équation personnelle, c'est-à-dire de la partie constante de l'erreur que commet un astronome dues toutes sortes d'observations.
		Bessel a résolu le problème difficile de la détermination de la parallaxe
	www.cosmovisions.com /Bessel.htm (464 words)

	CATHOLIC ENCYCLOPEDIA: Johann Franz Bessel
		On 7 February, 1714, he was elected Abbot of Göttweig, and from that time forward was commissioned by the emperor to conduct diplomatic negotiations, in addition to being made imperial theologian and serving twice as honorary rector of the University of Vienna.
		Abbot Bessel was the second founder of Göttweig, which became, under his rule of thirty-five years, a centre of learning.
		Personally, Abbot Bessel was a retiring religious, presenting to all a shining example of monastic piety and virtue.
	www.newadvent.org /cathen/02528a.htm (649 words)

	BESSEL FUNCTION - Online Information article about BESSEL FUNCTION
		He discussed their properties and constructed tables for their evaluation Although Bessel was the first to systematically treat of these functions, it is to be noted that in 1732 See also:
		The remarkable connexion between Bessel's functions and spherical harmonics was established in 1868 by F.
		Treatise on Bessel's Functions (1895); Encyclopddie der math.
	encyclopedia.jrank.org /BER_BLA/BESSEL_FUNCTION.html (519 words)

	Bessel Numbers, Borel Numbers. - Science Math Combinatorics (Site not responding. Last check: 2007-10-15)
		Let the Bessel number of the second kind B(n, k) be the number of set partitions of [n] into k blocks of size one or two, and let the Bessel number of the first kind b(n, k) be the coefficient of xn?k in ?y(n)?1(?x), where y(n)(x) is the nth Bessel polynomial.
		In this paper, we show that Bessel numbers satisfy two properties of Stirling numbers: The two kinds of Bessel numbers are related by inverse formulas, and both Bessel numbers of the first kind and the second kind form log-concave sequences.
		In this > paper, we show that Bessel numbers > satisfy two properties of Stirling numbers: The two kinds of Bessel > numbers are related by inverse > formulas, and both Bessel numbers of the first kind and the second kind > form log-concave sequences.
	www.okka.biz /_Bessel_Numbers__Borel_Numbers_-26283086-283-a.html (1541 words)

	Bessel function (Site not responding. Last check: 2007-10-15)
		Bessel was a mathematician who lived from 1784 to 1846.
		Sometimes the Bessel function is called the cylinder function.
		However, the Fourier transform of this 3d function, is a Bessel function of the first kind (of first order).
	www.2dcurves.com /gamma/gammabs.html (326 words)

	Bessel van der Kolk's Articles
		Bessel A. van der Kolk, MD, David Pelcovitz, PhD, Susan Roth, PhD, Francine S. Mandel, PhD, Alexander McFarlene, MD and Judith L. Herman, MD Exploring the Nature of Traumatic Memory: Combining Clinical Knowledge with Laboratory Methods Bessel A. van der Kolk, James W. Hopper, and Janet E. Osterman
		Bessel van der Kolk, MD The Compulsion to Repeat the Trauma Re-enactment, Revictimization, and Masochism
		Bessel A. van der Kolk, MD The Limits of Talk: Bessel van der Kolk wants to transform the treatment of trauma Mary Sykes Wylie
	home.earthlink.net /~hopefull/TC_Bessel_van_der_Kolk.htm (268 words)

	Bessel Functions (Site not responding. Last check: 2007-10-15)
		One of the varieties of special functions which are encountered in the solution of physical problems is the class of functions called Bessel functions.
		Bessel functions are encountered in physical situations where there is cylindrical symmetry.
		A specific class of special functions called spherical Bessel functions arises in problems of spherical symmetry like the spherical potential well in quantum mechanics.
	hyperphysics.phy-astr.gsu.edu /hbase/Math/bessel.html (173 words)

	Friedrich Wilhelm Bessel
		Warum ausgerechnet 61 Cygni für diese Untersuchung herhalten mußte, lag in seiner bemerkenswert hohen Eigenbewegung.
		Für Bessel ein Hinweis auf dessen relative Nähe, denn der Versuchsstern mußte nahe genug sein, da die Parallaxe sonst zu klein wäre, um noch zu verläßlichen Ergebnissen zu kommen.
		Friedrich Wilhelm Bessel hatte damit nicht nur das Werk von F. Herschel (1738-1822) vollendet.
	www.manfredholl.de /bessel.htm (742 words)

	Bessel Function
		In the Sturm-Liouville Boundary Value Problem, there is an important special case called Bessel's Differential Equation which arises in numerous problems, especially in polar and cylindrical coordinates.
		Since Bessel's differential equation is a second order ordinary differential equation, two sets of functions, the Bessel function of the first kind
		Recurrence Relation: A Bessel function of higher order can be expressed by Bessel functions of lower orders.
	www.efunda.com /math/bessel/bessel.cfm (352 words)

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