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Each section of data or output from formulas can be combined into an existing table or placed into a new table. Tables can be collected by the user onto single or multiple canvases. Whereas a typical Excel sheet has data strewn across it, a Numbers canvas could build the same output through smaller individual tables encompassing the same data. [9]
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.
Excel for the web is a free lightweight version of Microsoft Excel available as part of Office on the web, which also includes web versions of Microsoft Word and Microsoft PowerPoint. Excel for the web can display most of the features available in the desktop versions of Excel, although it may not be able to insert or edit them.
A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. A046758: Extravagant numbers: 4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, ... A number that has fewer digits than the number of digits in its prime factorization (including ...
The ability to chain formulas together is what gives a spreadsheet its power. Many problems can be broken down into a series of individual mathematical steps, and these can be assigned to individual formulas in cells. Some of these formulas can apply to ranges as well, like the SUM function that adds up all the numbers within a range.
There are various types of generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series. Every sequence in principle has a generating function of each type (except that Lambert and Dirichlet series require indices to start at 1 rather than 0), but the ease ...
Small multiple map series showing the trends in partisan voting margins in Utah, 1900–2012. Small multiples are a popular technique in cartographic design for multivariate mapping . As with the small multiple chart, each panel uses the same underlying two-dimensional space, but in this case that is a geographic space.
Therefore if a series is summable, any nonzero scalar multiple of the series is also summable and vice versa: if a series is divergent, then any nonzero scalar multiple of it is also divergent. Scalar multiplication of real numbers and complex numbers is associative, commutative, invertible, and it distributes over series addition.
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