|
Goodwin–Staton Integral
In mathematics, the Goodwin–Staton integral is defined as : Frank William John Olver (ed.), N. M. Temme (Chapter contr.), NIST Handbook of Mathematical Functions, Chapter 7, p160,Cambridge University Press Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessme ... 2010 : G(z)=\int_0^\infty \frac \, dt The integral satisfies the following third-order nonlinear differential equation： : 4w(z) +8\,z \frac w (z) + (2+2\,z^2) \frac w (z) +z \frac w \left( z \right) =0 Properties Symmetry: : G(-z)=-G(z) Expansion for small ''z'': : \begin G(z) = & 1-\gamma-\ln(z^2) -i\operatorname ( iz^2) \pi +\frac z \\ pt& \qquad + (-2 + \gamma + \ln(z^2) +i \operatorname (iz^2) \pi \Big) z^2 - \frac z^3 \\ pt& \qquad + \left( \frac 5 4 - \frac 1 2 \gamma - \frac 1 2 \ln (z^2) - \frac 1 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frank William John Olver
Frank William John Olver (December 15, 1924 – April 23, 2013) was a professor of mathematics at the Institute for Physical Science and Technology and Department of Mathematics at the University of Maryland who worked on asymptotic analysis, special functions, and numerical analysis. He was the editor in chief of the NIST Digital Library of Mathematical Functions. Awards 1969: Silver Medal of the US Department of Commerce 1974: Fellow of the U.K. Institute of Mathematics and its Applications 1996: Foreign Member of the Royal Society of Sciences, Uppsala, Sweden 2011: Gold Medal of the US Department of Commerce Publications * * * See also * Level-index arithmetic (LI) * Peter J. Olver (Son of Frank Olver) References * External linksFrank W. J. Olver, 1924-2013.SIAM News obituary by Roderick Wong an obituary in The Washington Post ''The Washington Post'', locally known as ''The'' ''Post'' and, informally, ''WaPo'' or ''WP'', is an American daily newspaper pub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessment to form Cambridge University Press and Assessment under Queen Elizabeth II's approval in August 2021. With a global sales presence, publishing hubs, and offices in more than 40 countries, it published over 50,000 titles by authors from over 100 countries. Its publications include more than 420 academic journals, monographs, reference works, school and university textbooks, and English language teaching and learning publications. It also published Bibles, runs a bookshop in Cambridge, sells through Amazon, and has a conference venues business in Cambridge at the Pitt Building and the Sir Geoffrey Cass Sports and Social Centre. It also served as the King's Printer. Cambridge University Press, as part of the University of Cambridge, was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Differential Equation
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a line ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
