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Joseph Ludwig Raabe
Joseph Ludwig Raabe (15 May 1801 in Brody, Galicia – 22 January 1859 in Zürich, Switzerland) was a Swiss mathematician. Life As his parents were quite poor, Raabe was forced to earn his living from a very early age by giving private lessons. He began to study mathematics in 1820 at the Polytechnicum in Vienna, Austria. In the autumn of 1831, he moved to Zürich, where he became professor of mathematics in 1833. In 1855, he became professor at the newly founded Swiss Polytechnicum. He is best known for Raabe's ratio test, an extension of d'Alembert's ratio test. Raabe's test serves to determine the convergence or divergence of an infinite series, in some cases. He is also known for the Raabe integral of the gamma function In mathematics, the gamma function (represented by Γ, capital Greek alphabet, Greek letter gamma) is the most common extension of the factorial function to complex numbers. Derived by Daniel Bernoulli, the gamma function \Gamma(z) is defined ...:. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divergent Series
In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit. If a series converges, the individual terms of the series must approach zero. Thus any series in which the individual terms do not approach zero diverges. However, convergence is a stronger condition: not all series whose terms approach zero converge. A counterexample is the harmonic series :1 + \frac + \frac + \frac + \frac + \cdots =\sum_^\infty\frac. The divergence of the harmonic series was proven by the medieval mathematician Nicole Oresme. In specialized mathematical contexts, values can be objectively assigned to certain series whose sequences of partial sums diverge, in order to make meaning of the divergence of the series. A ''summability method'' or ''summation method'' is a partial function from the set of series to values. For example, Cesàro summation assigns Grandi's divergent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Swiss Mathematicians
Swiss most commonly refers to: * the adjectival form of Switzerland *Swiss people Swiss may also refer to: Places * Swiss, Missouri * Swiss, North Carolina * Swiss, West Virginia * Swiss, Wisconsin Other uses * Swiss Café, an old café located in Baghdad, Iraq *Swiss-system tournament, in various games and sports * Swiss International Air Lines **Swiss Global Air Lines, a subsidiary *Swissair, former national air line of Switzerland * .swiss alternative TLD for Switzerland See also *Swiss made, label for Swiss products *Swiss cheese (other) *Switzerland (other) *Languages of Switzerland, none of which are called "Swiss" *International Typographic Style, also known as Swiss Style, in graphic design *Schweizer (other), meaning Swiss in German *Schweitzer Schweitzer is a surname. Notable people with the surname include: * Albert Schweitzer (1875–1965), German theologian, musician, physician, and medical missionary, winner of the 1952 Nobel Peace Priz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Brody
The term "the people" refers to the public or common mass of people of a polity. As such it is a concept of human rights law, international law as well as constitutional law, particularly used for claims of popular sovereignty. In contrast, a people is any plurality of persons considered as a whole. Used in politics and law, the term "a people" refers to the collective or community of an ethnic group or nation. Concepts Legal Chapter One, Article One of the Charter of the United Nations states that "peoples" have the right to self-determination. Though the mere status as peoples and the right to self-determination, as for example in the case of Indigenous peoples (''peoples'', as in all groups of indigenous people, not merely all indigenous persons as in ''indigenous people''), does not automatically provide for independent sovereignty and therefore secession. Indeed, judge Ivor Jennings identified the inherent problems in the right of "peoples" to self-determination, as i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1859 Deaths
Events January–March * January 21 – José Mariano Salas (1797–1867) becomes Conservative interim President of Mexico. * January 24 ( O. S.) – Under the rule of Alexandru Ioan Cuza, the provinces of Wallachia and Moldavia are united under the jurisdiction of the Ottoman Empire. It would be a principal step in forming the modern state of Romania. * January 28 – The city of Olympia is incorporated in the Washington Territory of the United States of America. * February 2 – Miguel Miramón (1832–1867) becomes Conservative interim President of Mexico. * February 4 – German scholar Constantin von Tischendorf rediscovers the '' Codex Sinaiticus'', a 4th-century uncial manuscript of the Greek Bible, in Saint Catherine's Monastery on the foot of Mount Sinai, in the Khedivate of Egypt and arranges for its presentation to his patron, Tsar Alexander II of Russia at Saint Petersburg. * February 14 – Oregon is admitted as the 33rd U.S. state. * February 12 – The Me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1801 Births
Events January–March *January 1 ** The legislative union of Great Britain and Ireland is completed under the Act of Union 1800, bringing about the United Kingdom of Great Britain and Ireland, and the abolition of the Parliament of Ireland. ** Giuseppe Piazzi discovers the asteroid and dwarf planet Ceres (dwarf planet), Ceres. *January 3 – Toussaint Louverture triumphantly enters Santo Domingo, the capital of the former Spanish Captaincy General of Santo Domingo, colony of Santo Domingo, which has become a colony of First French Empire, Napoleonic France. *January 31 – John Marshall is appointed Chief Justice of the United States. *February 4 – William Pitt the Younger resigns as Prime Minister of the United Kingdom. *February 9 – The Treaty of Lunéville ends the War of the Second Coalition between France and Austria. Under the terms of the treaty, all German territories left of the Rhine are officially annexed by France while Austria also has to recognize the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gamma Function
In mathematics, the gamma function (represented by Γ, capital Greek alphabet, Greek letter gamma) is the most common extension of the factorial function to complex numbers. Derived by Daniel Bernoulli, the gamma function \Gamma(z) is defined for all complex numbers z except non-positive integers, and for every positive integer z=n, \Gamma(n) = (n-1)!\,.The gamma function can be defined via a convergent improper integral for complex numbers with positive real part: \Gamma(z) = \int_0^\infty t^ e^\textt, \ \qquad \Re(z) > 0\,.The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic function, holomorphic except at zero and the negative integers, where it has simple Zeros and poles, poles. The gamma function has no zeros, so the reciprocal gamma function is an entire function. In fact, the gamma function corresponds to the Mellin transform of the negative exponential functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Series (mathematics)
In mathematics, a series is, roughly speaking, an addition of Infinity, infinitely many Addition#Terms, terms, one after the other. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures in combinatorics through generating functions. The mathematical properties of infinite series make them widely applicable in other quantitative disciplines such as physics, computer science, statistics and finance. Among the Ancient Greece, Ancient Greeks, the idea that a potential infinity, potentially infinite summation could produce a finite result was considered paradoxical, most famously in Zeno's paradoxes. Nonetheless, infinite series were applied practically by Ancient Greek mathematicians including Archimedes, for instance in the Quadrature of the Parabola, quadrature of the parabola. The mathematical side of Zeno's paradoxes was resolved using the concept of a limit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convergent Series
In mathematics, a series is the sum of the terms of an infinite sequence of numbers. More precisely, an infinite sequence (a_1, a_2, a_3, \ldots) defines a series that is denoted :S=a_1 + a_2 + a_3 + \cdots=\sum_^\infty a_k. The th partial sum is the sum of the first terms of the sequence; that is, :S_n = a_1 +a_2 + \cdots + a_n = \sum_^n a_k. A series is convergent (or converges) if and only if the sequence (S_1, S_2, S_3, \dots) of its partial sums tends to a limit; that means that, when adding one a_k after the other ''in the order given by the indices'', one gets partial sums that become closer and closer to a given number. More precisely, a series converges, if and only if there exists a number \ell such that for every arbitrarily small positive number \varepsilon, there is a (sufficiently large) integer N such that for all n \ge N, :\left , S_n - \ell \right , 1 produce a convergent series: *: ++++++\cdots = . * Alternating the signs of reciprocals of powers o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brody
Brody (, ; ; ; ) is a city in Zolochiv Raion, Lviv Oblast, Zolochiv Raion, Lviv Oblast, western Ukraine. It is located in the valley of the upper Styr, Styr River, approximately northeast of the oblast capital, Lviv. Brody hosts the administration of Brody urban hromada, one of the hromadas of Ukraine. Population: Brody is the junction of the Druzhba pipeline, Druzhba and Odesa–Brody pipeline, Odesa–Brody oil pipeline transport, pipelines. History The first mention of a settlement on the site of Brody is dated 1084 (Vladimir II Monomakh#Reign, Instructions by Vladimir Monomach). It is believed to have been destroyed by Batu Khan in 1241. Polish Kingdom From 1441 Brody was the property of different feudal families (Jan Sieniński; from 1511, Kamieniecki). Brody was granted Magdeburg rights, Magdeburg town rights by Polish King Stephen Báthory by virtue of a privilege (law), privilege issued in Lublin on 22 August 1584.Sadok Barącz, ''Wolne miasto handlowe Brody'', Lwów, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D'Alembert's Ratio Test
In mathematics, the ratio test is a test (or "criterion") for the convergence of a series :\sum_^\infty a_n, where each term is a real or complex number and is nonzero when is large. The test was first published by Jean le Rond d'Alembert and is sometimes known as d'Alembert's ratio test or as the Cauchy ratio test. The test The usual form of the test makes use of the limit The ratio test states that: * if ''L'' 1 then the series diverges; * if ''L'' = 1 or the limit fails to exist, then the test is inconclusive, because there exist both convergent and divergent series that satisfy this case. It is possible to make the ratio test applicable to certain cases where the limit ''L'' fails to exist, if limit superior and limit inferior are used. The test criteria can also be refined so that the test is sometimes conclusive even when ''L'' = 1. More specifically, let :R = \lim\sup \left, \frac\ :r = \lim\inf \left, \frac\. Then the ratio test states that: * if ''R'' 1, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
