An Etymological Dictionary of Astronomy and Astrophysics
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فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

M. Heydari-Malayeri    -    Paris Observatory

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Number of Results: 18 Search : series
Balmer series
  سری ِ بالمر   
seri-ye Bâlmer (#)

Fr.: série de Balmer   

A series of hydrogen → spectral lines (Hα, Hβ, Hγ, and others) that lies in the visible portion of the spectrum and results when electrons from upper → energy levels (n > 2) undergo → transition to n = 2.
Historically, Balmer emission lines (mainly Hα) from ionized nebulae were first observed by O. Struve and C. T. Elvey (1938, ApJ 88, 364). This was an important indication of the existence of hydrogen, in the ionized state, in the → interstellar medium.

Balmer; → series.

Brackett series
  سری ِ براکت   
seri-ye Brackett

Fr.: série de Brackette   

A series of lines in the infrared spectrum of atomic hydrogen due to electron jumps between the fourth and higher energy levels (Br α has wavelength 4.052 μm, Br γ 2.166 μm).

Named after the American physicist Frederick Brackett (1896-1980); → series.

complex Fourier series
  سری ِ فوریه‌ی ِ همتافت   
seri-ye Fourier-ye hamtâft

Fr.: série de Fourier complexe   

The complex notation for the → Fourier series of a function f(x). Using → Euler's formulae, the function can be written in cimplex form as f(x) = Σ cn einx (summed from -∞ to ∞), where the → Fourier coefficients are cn = (1/2π)∫ f(x) e-inx dx (integral from -π to +π).

complex; → Fourier series.

dominated series
  سری ِ چیریده   
seri-ye ciridé

Fr.: série dominée   

A → series if each of its → terms does not exceed, in absolute value, the corresponding term of some convergent numerical series with positive terms.

Dominated, p.p. of → dominate; → series.

finite series
  سری ِ کرانمند   
seri-ye karânmand (#)

Fr.: série finie   

A sum a1 + a2 + a3 + · · · + aN, where the ai's are real numbers. In terms of Σ-notation, it is written as a1 + a2 + a3 + · · · + aN = Σ (n = 1 to N).  See also → infinite series.

finite; → series.

Fourier series
  سری ِ فوریه   
seri-ye Fourier

Fr.: séries Fourier   

A mathematical tool used for decomposing a → periodic function into an infinite sum of sine and cosine functions. The general form of the Fourier series for a function f(x) with period 2π is:
(1/2) a0 + Σ (an cos (nx) + bn sin (nx), summed from n = 1 to ∞,
where an and bn are the → Fourier coefficients, measuring the strength of contribution from each harmonic. The functions cos (nx) and sin (nx) can be used in this way because they satisfy the → orthogonality conditions. For the problem of convergence of the Fourier series see → Dirichlet conditions. The Fourier series play a very important role in the study of periodic phenomena, because they allow one to decompose a large number of complex problems into simpler ones. The generalization of this method, called the → Fourier transform, makes it possible to also decompose non-periodic functions into harmonic components. See also → complex Fourier series, → Parseval's theorem.

Fourier analysis; → series.

harmonic series
  سری ِ هماهنگ   
seri-ye hamâhang

Fr.: série harmonique   

Overtones whose frequencies are integral multiples of the → fundamental frequency. The fundamental frequency is the first harmonic.

harmonic; → series.

Humphreys series
  سری ِ همفریز   
seri-ye Humphreys

Fr.: série de Humphreys   

A series of → spectral lines in the → infrared spectrum of → neutral hydrogen emitted by electrons in → excited states transitioning to the level described by the → principal quantum number  n = 6. It begins at 12368 nm (Hu α 12.37 microns) and has been traced to 3281.4 nm (3.28 microns).

Named after Curtis J. Humphreys (1898-1986), American physicist; → series.

infinite series
  سری ِ بیکران   
seri-ye bikarân (#)

Fr.: série infinie   

A series with infinitely many terms, in other words a series that has no last term, such as 1 + 1/4 + 1/9 + 1/16 + · · · + 1/n2 + ... . The idea of infinite series is familiar from decimal expansions, for instance the expansion π = 3.14159265358979... can be written as π = 3 + 1/10 + 4/102 + 1/103 + 5/104 + 9/105 + 2/106 + 6/107 + 5/108 + 3/109 + 5/1010 + 8/1011 + ... , so π is an "infinite sum" of fractions. See also → finite series.

infinite; → series.

Lyman series
  سری ِ لایمن   
seri-ye Lyman (#)

Fr.: séries de Lyman   

A series of lines in the spectrum of hydrogen, emitted when electrons jump from outer orbits to the first orbit. The Lyman series lies entirely within the ultraviolet region. The brightest lines are Lyman-alpha at 1216 Å, Lyman-beta at 1026 Å, and Lyman-gamma at 972 Å.

Lyman; → series.

Maclaurin series
  سری ِ مک‌لورن   
seri-ye Maclaurin

Fr.: série de Maclaurin   

A → Taylor series that is expanded about the reference point zero.

Named after Colin Maclaurin (1698-1746), a Scottish mathematician.

Paschen series
  سری ِ پاشن   
seri-ye Paschen (#)

Fr.: série de Paschen   

The spectral series associated with the third energy level of the hydrogen atom. The series lies in the infrared, with Pα at 18,751 Å, and Paschen limit at 8204 Å.

In honor of Friedrich Paschen (1865-1947), German physicist; → series.

Pfund series
  سری ِ پفوند   
seri-ye Pfund

Fr.: série de Pfund   

A series of lines in the infrared spectrum of atomic hydrogen whose representing transitions between the fifth energy level and higher levels.

After August Herman Pfund (1879-1949), an American physicist and spectroscopist; → series.

Pickering series
  سری ِ پیکرینگ   
seri-ye Pikering (#)

Fr.: série de Pickering   

A series of → spectral lines of → singly ionized helium, observed in very hot → O-type and → Wolf-Rayet stars associated with transitions between the → energy level with → principal quantum number n = 4 and higher levels: n = 4-5 (10124 Å), n = 4-7 (5412 Å), n = 4-9 (4541 Å), n = 4-9 (4522 Å), and n = 4-11 (4200 ˚). The 4-6 (6560 Å) and 4-8 (4859 Å) transitions were originally not included in this series because they coincided with the hydrogen → Balmer series of lines and were thus obscured.

In honor of Edward C. Pickering (1846-1919), American astronomer and physicist; → series.

power series
  سری ِ توانی   
seri-ye tavâni (#)

Fr.: série de puissance   

A series in which the terms contain regularly increasing powers of a variable. In general, a0 + a1x + a2x2 + ... + anxn, where a0, a1, etc. are constants.

power; → series.

series
  سری   
seri (#)

Fr.: série   

1) Math.: A sequence of numbers or mathematical expressions such as the n-th term may be written down in general form, and any particular term (say, the r-th) may be obtained by substituting r for n; e.g. xn is the general term of the series 1, x, x2, x3, ..., xn.
2) Electricity: An arrangement of the components, as resistors, connected along a single path, so the same current flows through all of the components. Compare → parallel.
3) → spectral series; → Lyman-alpha series.

From L. series "row, chain, series," from serere "to join, link, bind together," from PIE base *ser- "to line up, join."

Seri, loan from Fr.

spectral series
  سری ِ بینابی   
seri-ye binâbi

Fr.: série spectrale   

Spectral lines or group of lines occurring in sequence.

spectral; → series.

Taylor series
  سری ِ تیلر   
seri-ye Taylor (#)

Fr.: série de Taylor   

A series expansion of an infinitely differentiable function about a point a: Σ (1/n!) (x - a) n f n (a), where fn(a) is the n-th derivative of f at a, and the sum over n = 0 to ∞. If a = 0 the series is called a → Maclaurin series.

Named for the English mathematician Brook Taylor (1685-1731); → series.