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MediaWiki stores rendered formulas in a cache so that the images of those formulas do not need to be created each time the page is opened by a user. To force the rerendering of all formulas of a page, you must open it with the getter variables action=purge&mathpurge=true. Imagine for example there is a wrong rendered formula in the article Integral
The formula was first discovered by Abraham de Moivre [2] in the form ! [] +. De Moivre gave an approximate rational-number expression for the natural logarithm of the constant. Stirling's contribution consisted of showing that the constant is precisely 2 π {\displaystyle {\sqrt {2\pi }}} .
For the trivial case in which all the weights are equal to 1, the above formula is just like the regular formula for the variance of the mean (but notice that it uses the maximum likelihood estimator for the variance instead of the unbiased variance. I.e.: dividing it by n instead of (n-1)).
The Microsoft Excel spreadsheet program had a very elementary Y2K problem: Excel (in both Windows and Mac versions, when they are set to start at 1900) incorrectly set the year 1900 as a leap year for compatibility with Lotus 1-2-3. [30] In addition, the years 2100, 2200, and so on, were regarded as leap years.
To compute the integral, we set n to its value and use the reduction formula to express it in terms of the (n – 1) or (n – 2) integral. The lower index integral can be used to calculate the higher index ones; the process is continued repeatedly until we reach a point where the function to be integrated can be computed, usually when its index is 0 or 1.
Then the Selberg trace formula is given by = = () + {} () ( ()). The right hand side is a sum over conjugacy classes of the group Γ , with the first term corresponding to the identity element and the remaining terms forming a sum over the other conjugacy classes { T } (which are all hyperbolic in this case).
They did, making the IBM-compatible PC, running DOS, a de facto standard. The sales of MS-DOS (the version of DOS sold to customers other than IBM) made Microsoft a major player in the industry. [46] The press quickly identified Microsoft as being very influential on the IBM PC. PC Magazine asked if Gates was "the man behind the machine?". [41]
The word Brazil probably comes from the Portuguese word for brazilwood, a tree that once grew plentifully along the Brazilian coast. [31] In Portuguese, brazilwood is called pau-brasil, with the word brasil commonly given the etymology "red like an ember", formed from brasa ('ember') and the suffix -il (from -iculum or -ilium). [32]