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Fox H-function
In mathematics, the Fox H-function ''H''(''x'') is a generalization of the Meijer G-function and the Fox–Wright function introduced by . It is defined by a Mellin–Barnes integral : H_^ \!\left \begin ( a_1 , A_1 ) & ( a_2 , A_2 ) & \ldots & ( a_p , A_p ) \\ ( b_1 , B_1 ) & ( b_2 , B_2 ) & \ldots & ( b_q , B_q ) \end \right. \right= \frac\int_L \frac z^ \, ds, where ''L'' is a certain contour separating the poles of the two factors in the numerator. Compare to the Meijer G-function: : G_^ \!\left( \left. \begin a_1, \dots, a_p \\ b_1, \dots, b_q \end \; \ \, z \right) = \frac \int_L \frac \,z^s \,ds. The special case for which the Fox H reduces to the Meijer G is ''A''''j'' = ''B''''k'' = ''C'', ''C'' > 0 for ''j'' = 1...''p'' and ''k'' = 1...''q'' : : H_^ \!\left \begin ( a_1 , C ) & ( a_2 , C ) & \ldots & ( a_p , C ) \\ ( b_1 , C ) & ( b_2 , C ) & \ldots & ( b_q , C ) \end \right. \right= \frac G_^ \!\left( \left. \begin a_1, \dots, a_p \\ b_1, \dots, b_q \end ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meijer G-function
In mathematics, the G-function was introduced by as a very general function intended to include most of the known special functions as particular cases. This was not the only attempt of its kind: the generalized hypergeometric function and the MacRobert E-function had the same aim, but Meijer's G-function was able to include those as particular cases as well. The first definition was made by Meijer using a series; nowadays the accepted and more general definition is via a line integral in the complex plane, introduced in its full generality by Arthur Erdélyi in 1953. With the modern definition, the majority of the established special functions can be represented in terms of the Meijer G-function. A notable property is the closure of the set of all G-functions not only under differentiation but also under indefinite integration. In combination with a functional equation that allows to liberate from a G-function ''G''(''z'') any factor ''z''''ρ'' that is a constant power of its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fox–Wright Function
In mathematics, the Fox–Wright function (also known as Fox–Wright Psi function, not to be confused with Wright Omega function) is a generalisation of the generalised hypergeometric function ''p''''F''''q''(''z'') based on ideas of and : _p\Psi_q \left begin ( a_1 , A_1 ) & ( a_2 , A_2 ) & \ldots & ( a_p , A_p ) \\ ( b_1 , B_1 ) & ( b_2 , B_2 ) & \ldots & ( b_q , B_q ) \end ; z \right= \sum_^\infty \frac \, \frac . Upon changing the normalisation _p\Psi^*_q \left begin ( a_1 , A_1 ) & ( a_2 , A_2 ) & \ldots & ( a_p , A_p ) \\ ( b_1 , B_1 ) & ( b_2 , B_2 ) & \ldots & ( b_q , B_q ) \end ; z \right= \frac \sum_^\infty \frac \, \frac it becomes ''p''''F''''q''(''z'') for ''A''1...''p'' = B1...''q'' = 1. The Fox–Wright function is a special case of the Fox H-function : _p\Psi_q \left begin ( a_1 , A_1 ) & ( a_2 , A_2 ) & \ldots & ( a_p , A_p ) \\ ( b_1 , B_1 ) & ( b_2 , B_2 ) & \ldots & ( b_q , B_q ) \end ; z \right= H^_ \left \begin ( 1-a_1 , A_1 ) & ( 1-a_2 , A_2 ) & ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mellin–Barnes Integral
In mathematics, a Barnes integral or Mellin–Barnes integral is a contour integral involving a product of gamma functions. They were introduced by . They are closely related to generalized hypergeometric series. The integral is usually taken along a contour which is a deformation of the imaginary axis passing to the right of all poles of factors of the form Γ(''a'' + ''s'') and to the left of all poles of factors of the form Γ(''a'' − ''s''). Hypergeometric series The hypergeometric function is given as a Barnes integral by :_2F_1(a,b;c;z) =\frac \frac \int_^ \frac(-z)^s\,ds, see also . This equality can be obtained by moving the contour to the right while picking up the residues at ''s'' = 0, 1, 2, ... . for z\ll 1, and by analytic continuation elsewhere. Given proper convergence conditions, one can relate more general Barnes' integrals and generalized hypergeometric functions ''p''''F''''q'' in a similar way . Barnes lemmas The first Barnes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plot Of The Fox H Function H((((a 1,α 1),
Plot or Plotting may refer to: Art, media and entertainment * Plot (narrative), the story of a piece of fiction Music * ''The Plot'' (album), a 1976 album by jazz trumpeter Enrico Rava * The Plot (band), a band formed in 2003 Other * ''Plot'' (film), a 1973 French-Italian film * ''Plotting'' (video game), a 1989 Taito puzzle video game, also called Flipull * ''The Plot'' (video game), a platform game released in 1988 for the Amstrad CPC and Sinclair Spectrum * ''Plotting'' (non-fiction), a 1939 book on writing by Jack Woodford * ''The Plot'' (novel), a 2021 mystery by Jean Hanff Korelitz Graphics * Plot (graphics), a graphical technique for representing a data set * Plot (radar), a graphic display that shows all collated data from a ship's on-board sensors * Plot plan, a type of drawing which shows existing and proposed conditions for a given area Land * Plot (land), a piece of land used for building on ** Burial plot, a piece of land a person is buried in * Quadrat, a d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ram Kishore Saxena
Ram Kishore Saxena D.Sc , FNASc (11 November 1936) is an Indian mathematician and Emeritus professor, UGC Jai Narain Vyas University Jai Narain Vyas University (JNVU, formerly known as University of Jodhpur) is an educational institution in Jodhpur city in the Indian state of Rajasthan. Established in 1962, the university took over the four colleges of Jodhpur run by the sta ... and former Professor and Head, Department of Mathematics. Published work Saxena has published 356 research papers; under his supervision many scholars has done PhD and post-doctoral research. Saxena has published books. References Indian mathematicians Living people 1936 births {{India-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transactions Of The American Mathematical Society
The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 printed pages. See also * ''Bulletin of the American Mathematical Society'' * '' Journal of the American Mathematical Society'' * ''Memoirs of the American Mathematical Society'' * ''Notices of the American Mathematical Society'' * ''Proceedings of the American Mathematical Society'' External links * ''Transactions of the American Mathematical Society''on JSTOR JSTOR (; short for ''Journal Storage'') is a digital library founded in 1995 in New York City. Originally containing digitized back issues of academic journals, it now encompasses books and other primary sources as well as current issues of j ... American Mathematical Society academic journals Mathematics journals Publications established in 1900 {{math-journal-st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GitLab
GitLab Inc. is an open-core company that operates GitLab, a DevOps software package which can develop, secure, and operate software. The open source software project was created by Ukrainian developer Dmitriy Zaporozhets and Dutch developer Sytse Sijbrandij. In 2018, GitLab Inc. was considered the first partly-Ukrainian unicorn. Since its foundation, GitLab Inc. promoted remote work, and is known to be among the largest all-remote companies in the world. GitLab has an estimated 30 million registered users, with 1 million being active licensed users. Overview GitLab Inc. was established in 2014 to continue the development of the open-source code-sharing platform launched in 2011 by Dmitriy Zaporozhets. The company's other co-founder Sytse Sijbrandij initially contributed to the project and, by 2012, decided to build a business around it. GitLab offers its platform as a freemium. Since its foundation, GitLab Inc. has been an all-remote company. By 2020, the company employ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MathOverflow
MathOverflow is a mathematics question-and-answer (Q&A) website, which serves as an online community of mathematicians. It allows users to ask questions, submit answers, and rate both, all while getting merit points for their activities. It is a part of the Stack Exchange Network. It is primarily for asking questions on mathematics research – i.e. related to unsolved problems and the extension of knowledge of mathematics into areas that are not yet known – and does not welcome requests from non-mathematicians for instruction, for example homework exercises. It does welcome various questions on other topics that might normally be discussed among mathematicians, for example about publishing, refereeing, advising, getting tenure, etc. It is generally inhospitable to questions perceived as tendentious or argumentative. Origin and history The website was started by Berkeley graduate students and postdocs Anton Geraschenko, David Zureick-Brown, and Scott Morrison on 28 Septe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
