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In computer science, a lookup table (LUT) is an array that replaces runtime computation with a simpler array indexing operation, in a process termed as direct addressing.The savings in processing time can be significant, because retrieving a value from memory is often faster than carrying out an "expensive" computation or input/output operation. [1]
Use of a user-defined function sq(x) in Microsoft Excel. The named variables x & y are identified in the Name Manager. The function sq is introduced using the Visual Basic editor supplied with Excel. Subroutine in Excel calculates the square of named column variable x read from the spreadsheet, and writes it into the named column variable y.
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
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.
The formula for an integration by parts is () ′ = [() ()] ′ (). Beside the boundary conditions , we notice that the first integral contains two multiplied functions, one which is integrated in the final integral ( g ′ {\displaystyle g'} becomes g {\displaystyle g} ) and one which is differentiated ( f {\displaystyle f} becomes f ...
Vieta's formulas can equivalently be written as < < < (=) = for k = 1, 2, ..., n (the indices i k are sorted in increasing order to ensure each product of k roots is used exactly once). The left-hand sides of Vieta's formulas are the elementary symmetric polynomials of the roots.
In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.
A summation method that is linear and stable cannot sum the series 1 + 2 + 3 + ⋯ to any finite value. (Stable means that adding a term at the beginning of the series increases the sum by the value of the added term.) This can be seen as follows. If + + + =, then adding 0 to both sides gives