binomial series

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binomial series

[bī′nō·mē·əl ′sir·ēz]

(mathematics)

The expansion of (x + y) ⁿ when n is neither a positive integer nor zero. Also known as binomial expansion.

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The aim of this short article is to offer another proof of (1) and an extension of binomial series by means of telescoping method.

What is remarkable is that this identity generalizes, indeed, the well known binomial series because when c [right arrow] [infinity], it becomes

Telescopic approach to a formula of [sub.2][F.sub.1]-series by Gosper and Ebisu

Among specific topics are Archimedes and the geometric series to be, the binomial series in the hands of Euler, the Cauchy product, welcome to irrationals: the complete space of real numbers, and features of Ces[sz]ro and Abel means.

Infinite Series in a History of Analysis: Stages up to the Verge of Summability

As [beta] [right arrow] 0, expanding the square root in Equation (6) in its binomial series, we have [V.

An option value problem from Seinfeld

The sampling data was fitted to a Poisson and to a negative binomial series, respectively, by the dispersion index (I) and the dispersion parameter k, following Elliott (1983).

Spatial distribution of parasitism on Phyllocnistis citrella Stainton, 1856 (Lepidoptera: Gracillariidae) in citrus orchards/Distribuicao espacial do parasitismo Phyllocnistis citrella Stainton, 1856 (Lepidoptera: Gracillaridae) em pomares de citros

The product of the annual year coefficients from the two delta-lognormal model components, which individually indicated less decline than the unstandardized indices, provided final indices of abundance that declined 64% over the time series (due to the product of two positive fractional values <1 providing a even smaller value <1)--nearly identical to the unstandardized, Poisson, and negative binomial series (Fig.

The statistical properties of recreational catch rate data for some fish stocks off the northeast U.S. coast

They cover initial encounters with combinatorial reasoning; selections, arrangements, and distributions; binomial series and generating functions; alternating sums, the inclusion-exclusion principle, rook polynomials, and Fibonacci Nim; recurrence relations; special numbers; linear spaces and recurrence sequences; and counting with symmetries.