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Also, programs can be written that pull information from the worksheet, perform some calculations, and report the results back to the worksheet. In the figure, the name sq is user-assigned, and the function sq is introduced using the Visual Basic editor supplied with Excel. Name Manager displays the spreadsheet definitions of named variables x & y.
Exponential functions with bases 2 and 1/2. The exponential function is a mathematical function denoted by () = or (where the argument x is written as an exponent).Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
The Q-function can be generalized to higher dimensions: [14] = (),where (,) follows the multivariate normal distribution with covariance and the threshold is of the form = for some positive vector > and positive constant >.
In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution.Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions.
The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point. Uses of the Taylor series for analytic functions include: The partial sums (the Taylor polynomials) of the series can be used as approximations of the function ...
Repeated application of the recurrence relation for the lower incomplete gamma function leads to the power series expansion: [2] (,) = = (+) (+) = = (+ +). Given the rapid growth in absolute value of Γ(z + k) when k → ∞, and the fact that the reciprocal of Γ(z) is an entire function, the coefficients in the rightmost sum are well-defined, and locally the sum converges uniformly for all ...
The unsigned Stirling numbers of the first kind count the number of permutations of [n] with k cycles.A permutation is a set of cycles, and hence the set of permutations is given by
Power Query is built on what was then [when?] a new query language called M.It is a mashup language (hence the letter M) designed to create queries that mix together data. It is similar to the F Sharp programming language, and according to Microsoft it is a "mostly pure, higher-order, dynamically typed, partially lazy, functional language."