An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

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.

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.

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 c_n e^inx (summed from -∞ to ∞), where the → Fourier coefficients are c_n = (1/2π)∫ f(x) e^-inx dx (integral from -π to +π).

→ complex; → Fourier series.

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.

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

→ finite; → series.

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 (a_n cos (nx) + b_n sin (nx), summed from n = 1 to ∞,
where a_n and b_n 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.

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

→ harmonic; → series.

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.

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.

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.

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

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

A → time series consisting of two or more → univariate time series which share the same time period. As an example, if we record wind velocity and wind direction at the same instant of time, we have a multi-variate time series, specifically a bivariate one.

→ multivariate; → time; → series.

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.

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.

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.

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

→ power; → series.

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., as above.
Rise "string, thread, series," variant of rešte, → sequence.

Spectral lines or group of lines occurring in sequence.

→ spectral; → series.

A → time series if it obeys the following criteria: 1) Constant → mean over time (t). 2) Constant → variance for all t, and 3) The → autocovariance function between X_t1 and X_t2 only depends on the interval t₁ and t₂.

→ stationary; → time; → series.

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.