Balmer series 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 = |
Brackett series 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 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 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. |
dominated series 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. |
finite series seri-ye karânmand (#) Fr.: série finie A sum a_{1} + a_{2} + a_{3} + · · · + a_{N}, where the a_{i}'s are real numbers. In terms of Σ-notation, it is written as a_{1} + a_{2} + a_{3} + · · · + a_{N} = Σ (n = 1 to N). See also → infinite series. |
Fourier series 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: → Fourier analysis; → series. |
harmonic series seri-ye hamâhang Fr.: série harmonique Overtones whose frequencies are integral multiples of the → fundamental frequency. The fundamental frequency is the first harmonic. |
Humphreys series 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 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/n^{2} + ... . 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 + 4/10^{2} + 1/10^{3} + 5/10^{4} + 9/10^{5} + 2/10^{6} + 6/10^{7} + 5/10^{8} + 3/10^{9} + 5/10^{10} + 8/10^{11} + ... , so π is an "infinite sum" of fractions. See also → finite series. |
Lyman series 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. |
Maclaurin series 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. |
multivariate time series seri-ye zamâni-ye basvartâ Fr.: série temporelle multivariée 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. |
Paschen series 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 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 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 seri-ye tavâni (#) Fr.: série de puissance A series in which the terms contain regularly increasing powers of a variable. In general, a_{0} + a_{1}x + a_{2}x^{2} + ... + a_{n}x^{n}, where a_{0}, a_{1}, etc. are constants. |
series seri (#), rise (#) 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. x^{n} is the general term of the series
1, x, x^{2}, x^{3}, ..., x^{n}. 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. |
spectral series seri-ye binâbi Fr.: série spectrale Spectral lines or group of lines occurring in sequence. |
stationary time series seri-ye zamâni-ye istvar Fr.: série temporelle stationnaire 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 t_{1} and t_{2}. → stationary; → time; → series. |
Taylor series 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 f^{n}(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. |