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If the sum is of the form = ()where ƒ is a smooth function, we could use the Euler–Maclaurin formula to convert the series into an integral, plus some corrections involving derivatives of S(x), then for large values of a you could use "stationary phase" method to calculate the integral and give an approximate evaluation of the sum.
In mathematics, van der Corput's method generates estimates for exponential sums. The method applies two processes, the van der Corput processes A and B which relate the sums into simpler sums which are easier to estimate. The processes apply to exponential sums of the form = (())
The exponential function (in blue), and the sum of the first n + 1 terms of its power series (in red) where ! is the factorial of n (the ...
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function.
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
Hints and the solution for today's Wordle on Tuesday, January 14.
It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group. Let X be an n×n real or complex matrix. The exponential of X, denoted by e X or exp(X), is the n×n matrix given by the power series = =!
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