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In mathematics, a Newtonian series, named after Isaac Newton, is a sum over a sequence written in the form = = () = = ()! where is the ...
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
List of mathematical series; List of set identities and relations; List of alternative set theories; List of set theory topics; List of types of sets; List of shapes with known packing constant; List of solids derived from the sphere; List of mathematical spaces; List of spherical symmetry groups; List of textbooks in thermodynamics and ...
Finite differences are composed from differences in a sequence of values, or the values of a function sampled at discrete points. Finite differences are used both in interpolation and numerical analysis, and also play an important role in combinatorics and analytic number theory.
Newton's series may refer to: The Newton series for finite differences, used in interpolation theory. The binomial series, first proved by Isaac Newton.
(The series in t is a formal power series, but may alternatively be thought of as a series expansion for t sufficiently close to 0, for those more comfortable with that; in fact one is not interested in the function here, but only in the coefficients of the series.)
Newtonian cosmology; Newtonian dynamics; Newtonian fluid, a fluid that flows like water—its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear Non-Newtonian fluids, in which the viscosity changes with the applied shear force; Newtonian mechanics, also known as classical mechanics
It is assumed that the value of a function f defined on [,] is known at + equally spaced points: < < <.There are two classes of Newton–Cotes quadrature: they are called "closed" when = and =, i.e. they use the function values at the interval endpoints, and "open" when > and <, i.e. they do not use the function values at the endpoints.