|
Leo Pochhammer
Leo August Pochhammer (25 August 1841, Stendal – 24 March 1920, Kiel) was a Prussian mathematician who was known for his work on special functions and introduced the Pochhammer symbol, now generally used for expressing hypergeometric functions in a compact notation. Life Pochhammer was born in Stendal, but grew up in Berlin. He studied mathematics and physics at the Friedrich Wilhelm University in Berlin from 1859 to 1863. He received his doctorate in 1863 from Ernst Eduard Kummer. A period of habilitation followed in 1872. For the next two years he was a lecturer in Berlin. In 1874 he became Professor at the Christian Albrechts University in Kiel. After the Mathematical Seminar was founded at the same university in 1877, a second chair for mathematics was established with the appointment of Pochhammer as full professor. On 22 May 1877, regulations for the mathematical seminar at the Royal University in Kiel were issued. Along with the German mathematician and astronomer G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stendal
The Hanseatic City of Stendal () is a town in Saxony-Anhalt, Germany. It is the capital of the Stendal District and the unofficial capital of the Altmark region. Geography Situated west of the Elbe valley, the Stendal town centre is located some west of Berlin, around east of Hanover, and north of the state capital Magdeburg. Stendal is the seat of a University of Applied Sciences () and preserves a picturesque old town including a historic market and several churches. The nearby village Uchtspringe is home to a psychiatric rehabilitation clinic. Divisions The town Stendal consists of Stendal proper and the following 18 ''Ortschaften'' or municipal divisions:Hauptsatzung der Hansestadt Stendal November 2018. *Bindfelde *Borstel * [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Otto Toeplitz
Otto Toeplitz (1 August 1881 – 15 February 1940) was a German mathematician working in functional analysis., reprinted in Life and work Toeplitz was born to a Jewish family of mathematicians. Both his father and grandfather were ''Gymnasium'' mathematics teachers and published papers in mathematics. Toeplitz grew up in Breslau and graduated from the ''Gymnasium'' there. He then studied mathematics at the University of Breslau and was awarded a doctorate in algebraic geometry in 1905. In 1906 Toeplitz arrived at Göttingen University, which was then the world's leading mathematical center, and he remained there for seven years. The mathematics faculty included David Hilbert, Felix Klein, and Hermann Minkowski. Toeplitz joined a group of young people working with Hilbert: Max Born, Richard Courant and Ernst Hellinger, with whom he collaborated for many years afterward. At that time Toeplitz began to rework the theory of linear functionals and quadratic forms on ''n''-dimensi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From The Province Of Saxony
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] |
19th-century German Mathematicians
The 19th century began on 1 January 1801 (represented by the Roman numerals MDCCCI), and ended on 31 December 1900 (MCM). It was the 9th century of the 2nd millennium. It was characterized by vast social upheaval. Slavery was abolished in much of Europe and the Americas. The First Industrial Revolution, though it began in the late 18th century, expanded beyond its British homeland for the first time during the 19th century, particularly remaking the economies and societies of the Low Countries, France, the Rhineland, Northern Italy, and the Northeastern United States. A few decades later, the Second Industrial Revolution led to ever more massive urbanization and much higher levels of productivity, profit, and prosperity, a pattern that continued into the 20th century. The Catholic Church, in response to the growing influence and power of modernism, secularism and materialism, formed the First Vatican Council in the late 19th century to deal with such problems and confirm ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1920 Deaths
Events January * January 1 ** Polish–Soviet War: The Russian Red Army increases its troops along the Polish border from 4 divisions to 20. ** Kauniainen in Finland, completely surrounded by the city of Espoo, secedes from Espoo as its own market town. * January 7 – Russian Civil War: The forces of White movement, Russian White Admiral Alexander Kolchak surrender in Krasnoyarsk; the Great Siberian Ice March ensues. * January 10 ** The Treaty of Versailles takes effect, officially ending World War I. ** The League of Nations Covenant enters into force. On January 16, the organization holds its first council meeting, in Paris. * January 11 – The Azerbaijan Democratic Republic is recognised de facto by European powers in Palace of Versailles, Versailles. * January 13 – ''The New York Times'' Robert H. Goddard#Publicity and criticism, ridicules American rocket scientist Robert H. Goddard, which it will rescind following the launch of Apollo 11 in 1969. * Janua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1841 Births
Events January–March * January 20 – Charles Elliot of the United Kingdom and Qishan of the Qing dynasty agree to the Convention of Chuenpi. * January 26 – Britain occupies Hong Kong. Later in the year, the first census of the island records a population of about 7,500. * January 27 – The active volcano Mount Erebus in Antarctica is discovered, and named by James Clark Ross. * January 28 – Ross discovers the "Victoria Barrier", later known as the Ross Ice Shelf. On the same voyage, he discovers the Ross Sea, Victoria Land and Mount Terror. * January 30 – **El Salvador proclaims itself an independent republic, bringing an end to the Federal Republic of Central America. **A fire destroys two-thirds of the city of Mayagüez, Puerto Rico. * February 4 – The first known reference is made to Groundhog Day, celebrated in North America, in the diary of a James Morris. * February 10 – The Act of Union (''British North America Act'', 1840) is proclaimed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Falling And Rising Factorials
In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as the polynomial \begin (x)_n = x^\underline &= \overbrace^ \\ &= \prod_^n(x-k+1) = \prod_^(x-k) . \end The rising factorial (sometimes called the Pochhammer function, Pochhammer polynomial, ascending factorial, — A reprint of the 1950 edition by Chelsea Publishing. rising sequential product, or upper factorial) is defined as \begin x^ = x^\overline &= \overbrace^ \\ &= \prod_^n(x+k-1) = \prod_^(x+k) . \end The value of each is taken to be 1 (an empty product) when n=0. These symbols are collectively called factorial powers. The Pochhammer symbol, introduced by Leo August Pochhammer, is the notation (x)_n, where is a non-negative integer. It may represent ''either'' the rising or the falling factorial, with different articles and authors using different conventions. Pochhammer himself actually used (x)_n with yet another meaning, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pochhammer Contour
In mathematics, the Pochhammer contour, introduced by Jordan (1887), pp. 243–244 and , is a contour in the complex plane with two points removed, used for contour integration. If ''A'' and ''B'' are loops around the two points, both starting at some fixed point ''P'', then the Pochhammer contour is the commutator ''ABA''−1''B''−1, where the superscript −1 denotes a path taken in the opposite direction. With the two points taken as 0 and 1, the fixed basepoint ''P'' being on the real axis between them, an example is the path that starts at ''P'', encircles the point 1 in the counter-clockwise direction and returns to ''P'', then encircles 0 counter-clockwise and returns to ''P'', after that circling 1 and then 0 clockwise, before coming back to ''P''. The class of the contour is an actual commutator when it is considered in the fundamental group with basepoint ''P'' of the complement in the complex plane (or Riemann sphere) of the two points looped. When it come ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Q-Pochhammer Symbol
In the mathematical field of combinatorics, the ''q''-Pochhammer symbol, also called the ''q''-shifted factorial, is the product (a;q)_n = \prod_^ (1-aq^k)=(1-a)(1-aq)(1-aq^2)\cdots(1-aq^), with (a;q)_0 = 1. It is a ''q''-analog of the Pochhammer symbol (x)_n = x(x+1)\dots(x+n-1), in the sense that \lim_ \frac = (x)_n. The ''q''-Pochhammer symbol is a major building block in the construction of ''q''-analogs; for instance, in the theory of basic hypergeometric series, it plays the role that the ordinary Pochhammer symbol plays in the theory of generalized hypergeometric series. Unlike the ordinary Pochhammer symbol, the ''q''-Pochhammer symbol can be extended to an infinite product: (a;q)_\infty = \prod_^ (1-aq^k). This is an analytic function of ''q'' in the interior of the unit disk, and can also be considered as a formal power series in ''q''. The special case \phi(q) = (q;q)_\infty=\prod_^\infty (1-q^k) is known as Euler's function, and is important in combinatorics, number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Pochhammer Symbol
In mathematics, the generalized Pochhammer symbol of parameter \alpha>0 and partition \kappa=(\kappa_1,\kappa_2,\ldots,\kappa_m) generalizes the classical Pochhammer symbol, named after Leo August Pochhammer, and is defined as :(a)^_\kappa=\prod_^m \prod_^ \left(a-\frac+j-1\right). It is used in multivariate analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 .... References * Gamma and related functions Factorial and binomial topics {{numtheory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
German Imperial Naval Academy
The German Imperial Naval Academy (''Marineakademie'') at Kiel, Germany, was the higher education institution of the Imperial German Navy, ''Kaiserliche Marine'', where naval officers were prepared for service in the higher levels of command, from 1872 until 1910. The Naval Academy was founded in 1872 by the Chief of the Imperial Admiralty, Lieutenant General Albrecht von Stosch, as a graduate school to prepare naval officers selected for higher duties in the Imperial Navy. He took as a model the Prussian Military Academy, which trained general staff officers for the Prussian Army. The curriculum consisted of navy subjects such as naval history and general education courses. In addition, course participants learned two modern foreign languages. Initially the training lasted for three years; beginning in 1883 it was shortened to two years. The Naval Academy was the training command of the Imperial Navy. From 1888 the Naval Academy was in the same building as the undergraduate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kiel
Kiel ( ; ) is the capital and most populous city in the northern Germany, German state of Schleswig-Holstein. With a population of around 250,000, it is Germany's largest city on the Baltic Sea. It is located on the Kieler Förde inlet of the Bay of Kiel and lies in the southeast of the Jutland Peninsula, on the mouth of the Schwentine River, approximately northeast of Hamburg. The world's busiest artificial waterway, the Kiel Canal, has a terminus in Kiel's Holtenau district. This canal connects the Baltic to the North Sea, with its other end in Brunsbüttel. Most of Kiel is part of Holstein. The boroughs north of the Schwentine also belong to Wagria, while those north of the Kiel Canal are historically part of Southern Schleswig. Kiel is one of Germany's major maritime centres, known for a variety of international sailing events, including the annual Kiel Week, which is the biggest sailing event in the world. Kiel is also known for the Kiel mutiny, Kiel Mutiny, when sailors re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
