Absolute convergenceIn mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite. More precisely, a real or complex series is said to converge absolutely if for some real number Similarly, an improper integral of a function, is said to converge absolutely if the integral of the absolute value of the integrand is finite—that is, if Absolute convergence is important for the study of infinite series because its definition is strong enough to have properties of finite sums that not all convergent series possess – a convergent series that is not absolutely convergent is called conditionally convergent, while absolutely convergent series behave "nicely".
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.
Taylor seriesIn mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century.
Madhava seriesIn mathematics, a Madhava series is one of the three Taylor series expansions for the sine, cosine, and arctangent functions discovered in 14th or 15th century Kerala by the mathematician and astronomer Madhava of Sangamagrama (c. 1350 – c. 1425) or his followers in the Kerala school of astronomy and mathematics. Using modern notation, these series are: All three series were later independently discovered in 17th century Europe.
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.
Augustin-Louis CauchyBaron Augustin-Louis Cauchy (UKˈkoʊʃi,_ˈkaʊʃi , USkoʊˈʃiː , oɡystɛ̃ lwi koʃi; 21 August 1789 - 23 May 1857) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics. He was one of the first to state and rigorously prove theorems of calculus, rejecting the heuristic principle of the generality of algebra of earlier authors. He (nearly) single-handedly founded complex analysis and the study of permutation groups in abstract algebra.
