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In mathematics, the Euler–Maclaurin formula is a formula for the difference between an integral and a closely related sum. It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using integrals and the machinery of calculus. For example, many asymptotic expansions are derived from the ...
e. In linguistics, an intensifier (abbreviated INT) is a lexical category (but not a traditional part of speech) for a modifier that makes no contribution to the propositional meaning of a clause but serves to enhance and give additional emotional context to the lexical item it modifies. Intensifiers are grammatical expletives, specifically ...
A summation-by-parts (SBP) finite difference operator conventionally consists of a centered difference interior scheme and specific boundary stencils that mimics behaviors of the corresponding integration-by-parts formulation. [3][4] The boundary conditions are usually imposed by the Simultaneous-Approximation-Term (SAT) technique. [5] The ...
Comparison (grammar) Comparison is a feature in the morphology or syntax of some languages whereby adjectives and adverbs are rendered in an inflected or periphrastic way to indicate a comparative degree, property, quality, or quantity of a corresponding word, phrase, or clause. A superlative construction expresses the greatest quality ...
Upper and lower methods make the approximation using the largest and smallest endpoint values of each subinterval, respectively. The values of the sums converge as the subintervals halve from top-left to bottom-right. In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum.
Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.
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