Power seriesIn mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions. In fact, Borel's theorem implies that every power series is the Taylor series of some smooth function. In many situations, c (the center of the series) is equal to zero, for instance when considering a Maclaurin series.
Jean le Rond d'AlembertJean-Baptiste le Rond d'Alembert (dæləmˈbɛər; ʒɑ̃ batist lə ʁɔ̃ dalɑ̃bɛːʁ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the Encyclopédie. D'Alembert's formula for obtaining solutions to the wave equation is named after him. The wave equation is sometimes referred to as d'Alembert's equation, and the fundamental theorem of algebra is named after d'Alembert in French.
Harmonic analysisHarmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on the real line, or by Fourier series for periodic functions. Generalizing these transforms to other domains is generally called Fourier analysis, although the term is sometimes used interchangeably with harmonic analysis.
Philosophy of mathematicsThe philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics makes this branch of philosophy broad and unique. The philosophy of mathematics has two major themes: mathematical realism and mathematical anti-realism. The origin of mathematics is of arguments and disagreements.
Riemann series theoremIn mathematics, the Riemann series theorem, also called the Riemann rearrangement theorem, named after 19th-century German mathematician Bernhard Riemann, says that if an infinite series of real numbers is conditionally convergent, then its terms can be arranged in a permutation so that the new series converges to an arbitrary real number, or diverges. This implies that a series of real numbers is absolutely convergent if and only if it is unconditionally convergent.
Unconditional convergenceIn mathematics, specifically functional analysis, a series is unconditionally convergent if all reorderings of the series converge to the same value. In contrast, a series is conditionally convergent if it converges but different orderings do not all converge to that same value. Unconditional convergence is equivalent to absolute convergence in finite-dimensional vector spaces, but is a weaker property in infinite dimensions. Let be a topological vector space.
Rate of convergenceIn numerical analysis, the order of convergence and the rate of convergence of a convergent sequence are quantities that represent how quickly the sequence approaches its limit. A sequence that converges to is said to have order of convergence and rate of convergence if The rate of convergence is also called the asymptotic error constant. Note that this terminology is not standardized and some authors will use rate where this article uses order (e.g., ).
Uniform convergenceIn the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions converges uniformly to a limiting function on a set as the function domain if, given any arbitrarily small positive number , a number can be found such that each of the functions differs from by no more than at every point in .
2008–09 Pittsburgh Penguins seasonThe 2008–09 Pittsburgh Penguins season was the 42nd season of Pittsburgh Penguins in the National Hockey League (NHL). The regular season began with two games against the Ottawa Senators in Stockholm, Sweden on October 4 and October 5, 2008. On February 15, the team had a record of 27–25–5 and was five points out of playoff position. The organization fired head coach Michel Therrien and replaced him with Dan Bylsma, head coach of the organization's American Hockey League affiliate in Wilkes-Barre.
RAF JurbyRoyal Air Force Station Jurby or more simply RAF Jurby is a former Royal Air Force station built in the north west of the Isle of Man. It was opened in 1939 on of land acquired by the Air Ministry in 1937, under the control of No. 29 Group, RAF. During the Second World War the station was used for training as No. 5 Armament Training Station, No. 5 Air Observer School, No. 5 Bombing & Gunnery School and the No. 5 Air Navigation & Bombing School. In addition RAF Jurby also played host to a variety of operational squadrons.
1&1 AG1&1 AG (known until June 2, 2021 as: 1&1 Drillisch Aktiengesellschaft) is a German telecommunications service provider headquartered in Maintal, Rhineland-Palatinate and listed on the TecDAX. Since 2017, the majority of the company has belonged to United Internet, and offers both mobile and landline services. At the end of 2021, 1&1 employed 3,167 people and reported profits of 3.91 billion Euros by the end of the fiscal year. As of December 31, 2021, 1&1 had about 15.4 million customer contracts, 11.
9th Cavalry Regiment (United States)The 9th Cavalry Regiment is a parent cavalry regiment of the United States Army. It is not related to the 9th Kansas Cavalry Regiment of the Union Army. Historically, it was one of the Army's four segregated African-American regiments and was part of what was known as the Buffalo Soldiers. The regiment saw combat during the Indian and Spanish–American Wars. During Westward Expansion, the regiment provided escort for the early western settlers and maintained peace on the American frontier.
