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In mathematics, a telescoping series is a series whose general term is of the form = +, i.e. the difference of two consecutive terms of a sequence (). As a consequence the partial sums of the series only consists of two terms of ( a n ) {\displaystyle (a_{n})} after cancellation.
Whereas the objective function in a linear program is a linear function, the objective function in a linear-fractional program is a ratio of two linear functions. A linear program can be regarded as a special case of a linear-fractional program in which the denominator is the constant function 1. Formally, a linear-fractional program 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.
A series of functions in which the terms are trigonometric functions is called a trigonometric series: + = ( + ). The most important example of a trigonometric series is the Fourier series of a function.
Given some initial conditions, we can either solve the recurrence entirely or obtain a solution in power series form. Since the ratio of coefficients A k / A k − 1 {\displaystyle A_{k}/A_{k-1}} is a rational function , the power series can be written as a generalized hypergeometric series .
With four teams on a bye for Week 10, Sunday's slate of games will be slightly thinner than usual.However, that doesn't mean this week is devoid of exciting matchups. Fans can look forward to 12 ...
These cozy breakfast recipes, like sweet potato toast and oatmeal, take under 20 minutes to prepare for a warm and nourishing meal to start your day.
The final rosters for the 4 Nations Face-Off international tournament were unveiled on Wednesday as the NHL prepares for its first best-on-best tournament since the 2016 World Cup of Hockey.
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