Results 261 to 270 of about 537,485 (280)

Analogs of recurrent Newton formulas

Russian Mathematics, 2009
For a system of algebraic equations, the recurrent Newton formulas for evaluating power sums of roots in terms of coefficients are well-known. In this paper, analogs of these formulas are obtained for nonlinear nonalgebraic equations. The main idea is to study sums of negative powers of roots.
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An Extension of the Leibniz-Newton Formula

2004
In this section we are going to present a slight extension of the Leibniz-Newton formula for the computation of the definite integral, an extension that can be applied also in the case of some integrable functions which do not admit ...
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Newton's Formula and the Continued Fraction Expansion of √d

Experimental Mathematics, 2001
It is known that if the period s(d) of the continued fraction expansion of √d satisfies s(d) ≤ 2, then all Newton's approximants are convergents of √d, and moreover Rn = P2n+1/q2n+1 for all n ≥ 0. Motivated by this fact we define j = j(d, n) by Rn = P2n+1+2j/ q2n+1+2j if Rn is a convergent of √d, and define b = b(d) by b = |{n : 0 ≤ n ≤ s-1 and Rn is a
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Generalized Newton–Leibniz Formula

2016
One of the (if not the) most important theorems of classical analysis is the Newton–Leibniz formula: $$\displaystyle{ \int _{a}^{b}f\ dx = F(b) - F(a), }$$ allowing us to compute many integrals. The purpose of this chapter is to extend its validity to Lebesgue integrable functions.
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Thermodynamically consistent quasi‐Newton formulae

AIChE Journal, 1985
AbstractNewton and quasi‐Newton methods have been used in chemical process design and optimization calculations for quite some time. They continue to be used today, both in the traditional sense and as part of the more recent hybrid method. While Newton‐based fixed‐point methods have been used to solve many different kinds of chemical process design ...
Angelo Lucia, D. C. Miller, Ashwani Kumar   +2 more
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On the Error Analysis Associated with the Newton-Cotes Formulae

International Journal of Computer Mathematics, 2002
In the current paper, the truncation error (TE) for both the closed and open Newton-Cotes quadrature formulae for numerical integration is investigated and calculated for n = 1, 2, @, 12 in both cases.
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Newton's Interpolation Formulas. An unpublished Manuscript of Sir Isaac Newton

Journal of the Institute of Actuaries, 1927
The mortality of Europeans in West Africa has on several occasions been the subject of discussion in this Institute or of note in the pages of the Journal. In 1886 Dr. T. B. Sprague read a paper on the mortality of Europeans in the Congo, based on the statistics from Stanley's work on the Pounding of the Free State: In 1892 Dr. T. G. Lyon contributed a
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An Application of Newton's Power-Sum Formulas

The American Mathematical Monthly, 1949
(1949). An Application of Newton's Power-Sum Formulas. The American Mathematical Monthly: Vol. 56, No. 6, pp. 377-379.
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On Average Newton-Cotes Quadrature Formulas

IMA Journal of Applied Mathematics, 1978
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NEWTON POLYHEDRA AND THE EULER-JACOBI FORMULA

Russian Mathematical Surveys, 1978
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