“series”的概念、定义、翻译、参考文献-科学参考

series

Physics

A sequence of terms each of which can be written in a form that is an algebraic function of its position in the series. For example, the exponential series 1+x+x²/2!+x³/3! +…has an nth term xⁿ/n!. The sum of all the terms from n=0 to n=∞ is written:

$Σ_{v = 0}^{\infty} = x^{n} / n!$

This series has an infinite number of terms and is therefore called an infinite series. A finite series has a fixed number of terms. See also asymptotic series; convergent series.

Mathematics

A finite series of length n is written as a₁+a₂+…+a_n, where a₁, a₂,…, a_n are n numbers called the terms in the series. The sum of the series is simply the sum of the n terms.

An infinite series is written as a₁+a₂+a₃+…, with terms a₁, a₂, a₃,…, one corresponding to each positive integer. The nth partial sum is s_n, the sum of the first n terms. If the sequence s₁, s₂, s₃,…has a limit s, then the value s is called the sum (or sum to infinity) of the infinite series. Otherwise, the infinite series is said to diverge. For a list of important series and convergence tests, see appendix 11 and appendix 12. See also algebra of limits, arithmetic series, geometric series, partial sum, Taylor series.

Statistics

See reliability theory.

Electronics and Electrical Engineering

Circuit elements are said to be in series if they are connected so that one current flows in turn through each of them (see diagram).
For n resistors in series the total resistance, R, is given by:
$R = r_{1} + r_{2} + \dots r_{n}$
where r₁, r₂, …r_n are the values of the individual resistors. The resistors thus behave collectively as one large resistance.
For n capacitors in series the total capacitance, C, is given by:
$\frac{1}{C} = \frac{1}{c_{1}} + \frac{1}{c_{2}} + \dots \frac{1}{c_{n}}$
where c₁, c₂, …c_n are the individual capacitances.
Machines, transformers, and cells are said to be in series when terminals of opposite polarity are connected together to form a chain. Several cells connected together in series add the values of the emfs and can therefore supply a larger voltage.
Compare parallel.

Geology and Earth Sciences

The major subdivision of a system, and the chronostratigraphic equivalent of an epoch. It denotes the layers of strata or the body of rock formed during one epoch. A series may itself be divided into stages. When used formally the initial letter of the term is often capitalized, e.g. Lower Cretaceous Series.

单词	series
释义	series Physics A sequence of terms each of which can be written in a form that is an algebraic function of its position in the series. For example, the exponential series 1+x+x²/2!+x³/3! +…has an nth term xⁿ/n!. The sum of all the terms from n=0 to n=∞ is written: $Σ_{v = 0}^{\infty} = x^{n} / n!$ This series has an infinite number of terms and is therefore called an infinite series. A finite series has a fixed number of terms. See also asymptotic series; convergent series. Mathematics A finite series of length n is written as a₁+a₂+…+a_n, where a₁, a₂,…, a_n are n numbers called the terms in the series. The sum of the series is simply the sum of the n terms. An infinite series is written as a₁+a₂+a₃+…, with terms a₁, a₂, a₃,…, one corresponding to each positive integer. The nth partial sum is s_n, the sum of the first n terms. If the sequence s₁, s₂, s₃,…has a limit s, then the value s is called the sum (or sum to infinity) of the infinite series. Otherwise, the infinite series is said to diverge. For a list of important series and convergence tests, see appendix 11 and appendix 12. See also algebra of limits, arithmetic series, geometric series, partial sum, Taylor series. Statistics See reliability theory. Electronics and Electrical Engineering Circuit elements are said to be in series if they are connected so that one current flows in turn through each of them (see diagram). For n resistors in series the total resistance, R, is given by: $R = r_{1} + r_{2} + \dots r_{n}$ where r₁, r₂, …r_n are the values of the individual resistors. The resistors thus behave collectively as one large resistance. For n capacitors in series the total capacitance, C, is given by: $\frac{1}{C} = \frac{1}{c_{1}} + \frac{1}{c_{2}} + \dots \frac{1}{c_{n}}$ where c₁, c₂, …c_n are the individual capacitances. Machines, transformers, and cells are said to be in series when terminals of opposite polarity are connected together to form a chain. Several cells connected together in series add the values of the emfs and can therefore supply a larger voltage. Compare parallel. Geology and Earth Sciences The major subdivision of a system, and the chronostratigraphic equivalent of an epoch. It denotes the layers of strata or the body of rock formed during one epoch. A series may itself be divided into stages. When used formally the initial letter of the term is often capitalized, e.g. Lower Cretaceous Series.
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