|
Harry Pollard (mathematician)
Harry Pollard (28 February 1919 – November 20, 1985). was an American mathematician. He received his Ph.D from Harvard University in 1942 under the supervision of David Widder. He then taught at Cornell University, and was Professor of Mathematics at Purdue University from 1961 until his death in 1985. He is known for his work on celestial mechanics, orthogonal polynomials and the n-body problem as well as for the several textbooks he authored or co-authored. In the theory of Orthogonal polynomials, Pollard solved a conjecture of Antoni Zygmund, establishing mean convergence of the partial sums in L^p norms for the Legendre polynomials and Jacobi polynomials in a series of three papers in the Transactions of the American Mathematical Society. The first of these papers deals with the fundamental case of Legendre polynomials In mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University
Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyman John Harvard (clergyman), John Harvard, it is the oldest institution of higher learning in the United States. Its influence, wealth, and rankings have made it one of the most prestigious universities in the world. Harvard was founded and authorized by the Massachusetts General Court, the governing legislature of Colonial history of the United States, colonial-era Massachusetts Bay Colony. While never formally affiliated with any Religious denomination, denomination, Harvard trained Congregationalism in the United States, Congregational clergy until its curriculum and student body were gradually secularized in the 18th century. By the 19th century, Harvard emerged as the most prominent academic and cultural institution among the Boston B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Legendre Polynomials
In mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number of mathematical properties and numerous applications. They can be defined in many ways, and the various definitions highlight different aspects as well as suggest generalizations and connections to different mathematical structures and physical and numerical applications. Closely related to the Legendre polynomials are associated Legendre polynomials, Legendre functions, Legendre functions of the second kind, big q-Legendre polynomials, and associated Legendre functions. Definition and representation Definition by construction as an orthogonal system In this approach, the polynomials are defined as an orthogonal system with respect to the weight function w(x) = 1 over the interval [-1,1]. That is, P_n(x) is a polynomial of degree n, such that \int_^1 P_m(x) P_n(x) \,dx = 0 \quad \text n \ne m. With the additional standardi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Textbook Writers
American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, people who self-identify their ancestry as "American" ** American English, the set of varieties of the English language native to the United States ** Native Americans in the United States, indigenous peoples of the United States * American, something of, from, or related to the Americas, also known as "America" ** Indigenous peoples of the Americas * American (word), for analysis and history of the meanings in various contexts Organizations * American Airlines, U.S.-based airline headquartered in Fort Worth, Texas * American Athletic Conference, an American college athletic conference * American Recordings (record label), a record label that was previously known as Def American * American University, in Washington, D.C. Sports teams S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard Graduate School Of Arts And Sciences Alumni
Harvard University is a private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher learning in the United States. Its influence, wealth, and rankings have made it one of the most prestigious universities in the world. Harvard was founded and authorized by the Massachusetts General Court, the governing legislature of colonial-era Massachusetts Bay Colony. While never formally affiliated with any denomination, Harvard trained Congregational clergy until its curriculum and student body were gradually secularized in the 18th century. By the 19th century, Harvard emerged as the most prominent academic and cultural institution among the Boston elite. Following the American Civil War, under Harvard president Charles William Eliot's long tenure from 1869 to 1909, Harvard developed multiple professional schools, which transform ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1985 Deaths
The year 1985 was designated as the International Youth Year by the United Nations. Events January * January 1 ** The Internet's Domain Name System is created. ** Greenland withdraws from the European Economic Community as a result of a new agreement on fishing rights. * January 7 – Japan Aerospace Exploration Agency launches '' Sakigake'', Japan's first interplanetary spacecraft and the first deep space probe to be launched by any country other than the United States or the Soviet Union. * January 15 – Tancredo Neves is elected president of Brazil by the Congress, ending the 21-year military rule. * January 27 – The Economic Cooperation Organization (ECO) is formed, in Tehran. * January 28 – The charity single record "We Are the World" is recorded by USA for Africa. February * February 4 – The border between Gibraltar and Spain reopens for the first time since Francisco Franco closed it in 1969. * February 5 – Australia cancels its involv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1919 Births
Events January * January 1 ** The Czechoslovak Legions occupy much of the self-proclaimed "free city" of Bratislava, Pressburg (later Bratislava), enforcing its incorporation into the new republic of Czechoslovakia. ** HMY Iolaire, HMY ''Iolaire'' sinks off the coast of the Hebrides; 201 people, mostly servicemen returning home to Lewis and Harris, are killed. * January 2–January 22, 22 – Russian Civil War: The Red Army's Caspian-Caucasian Front begins the Northern Caucasus Operation (1918–1919), Northern Caucasus Operation against the White Army, but fails to make progress. * January 3 – The Faisal–Weizmann Agreement is signed by Faisal I of Iraq, Emir Faisal (representing the Arab Kingdom of Hejaz) and Zionism, Zionist leader Chaim Weizmann, for Arab–Jewish cooperation in the development of a Jewish homeland in Palestine (region), Palestine, and an Arab nation in a large part of the Middle East. * January 5 – In Germany: ** Spartacist uprising in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carus Mathematical Monographs
The ''Carus Mathematical Monographs'' is a monograph series published by the Mathematical Association of America.Drake, Miriam A. (2003). ''Encyclopedia of Library and Information Science: Lib-Pub.'' CRC Press, Books in this series are intended to appeal to a wide range of readers in mathematics and science. Scope and audience While the books are intended to cover nontrivial material, the emphasis is on exposition and clear communication rather than novel results and a systematic Bourbaki-style presentation. The webpage for the series states: The exposition of mathematical subjects that the monographs contain are set forth in a manner comprehensible not only to teachers and students specializing in mathematics, but also to scientific workers in other fields. More generally, the monographs are intended for the wide circle of thoughtful people familiar with basic graduate or advanced undergraduate mathematics encountered in the study of mathematics itself or in the context of rela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacobi Polynomials
In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) P_n^(x) are a class of Classical orthogonal polynomials, classical orthogonal polynomials. They are orthogonal with respect to the weight (1-x)^\alpha(1+x)^\beta on the interval [-1,1]. The Gegenbauer polynomials, and thus also the Legendre polynomials, Legendre, Zernike polynomials, Zernike and Chebyshev polynomials, are special cases of the Jacobi polynomials. The Jacobi polynomials were introduced by Carl Gustav Jacob Jacobi. Definitions Via the hypergeometric function The Jacobi polynomials are defined via the hypergeometric function as follows: :P_n^(z)=\frac\,_2F_1\left(-n,1+\alpha+\beta+n;\alpha+1;\tfrac(1-z)\right), where (\alpha+1)_n is Pochhammer symbol, Pochhammer's symbol (for the rising factorial). In this case, the series for the hypergeometric function is finite, therefore one obtains the following equivalent expression: :P_n^ (z) = \frac \sum_^n \frac \left(\frac\right)^m. R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antoni Zygmund
Antoni Zygmund (December 26, 1900 – May 30, 1992) was a Polish-American mathematician. He worked mostly in the area of mathematical analysis, including harmonic analysis, and he is considered one of the greatest analysts of the 20th century. Zygmund was responsible for creating the Chicago school of mathematical analysis together with his doctoral student Alberto Calderón, for which he was awarded the National Medal of Science in 1986. Biography Born in Warsaw, Zygmund obtained his Ph.D. from the University of Warsaw (1923) and was a professor at Stefan Batory University at Wilno from 1930 to 1939, when World War II broke out and Poland was occupied. In 1940 he managed to emigrate to the United States, where he became a professor at Mount Holyoke College in South Hadley, Massachusetts. In 1945–1947 he was a professor at the University of Pennsylvania, and from 1947, until his retirement, at the University of Chicago. He was a member of several scientific societies. Fro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Widder
David Vernon Widder (25 March 1898 – 8 July 1990) was an American mathematician. He earned his Ph.D. at Harvard University in 1924 under George Birkhoff and went on to join the faculty there. He was a co-founder of the ''Duke Mathematical Journal'' and the author of the textbook ''Advanced Calculus'' (Prentice-Hall, 1947). He wrote also '' The Laplace transform'' (in which he gave a first solution to Landau's problem on the Dirichlet eta function), (pbk reprint of 1941 1st edition) ''An introduction to transform theory'', and '' The convolution transform'' (co-author with I. I. Hirschman). References *''A Century of Mathematics in America'' by Peter L. Duren and Richard Askey Richard Allen Askey (June 4, 1933 – October 9, 2019) was an American mathematician, known for his expertise in the area of special functions. The Askey–Wilson polynomials (introduced by him in 1984 together with James A. Wilson) are on the ..., American Mathematical Society, 1988, . *''A Hist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
