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Longer titles found: Divergent geometric series (view)

searching for Geometric series 68 found (238 total)

Relative species abundance (2,589 words) [view diff] exact match in snippet view article find links to article

I. Motomura developed the geometric series model based on benthic community data in a lake. Within the geometric series each species' level of abundance

Van Wijngaarden transformation (315 words) [view diff] exact match in snippet view article find links to article

by bringing them in a row. (For example, this will be needed in a geometric series with ratio − 4 {\displaystyle -4} .) This process of successive averaging

E (mathematical constant) (6,377 words) [view diff] exact match in snippet view article

expression for a geometric series] &c. major est. … si a = b, debebitur plu quam 2½a & minus quam 3a." ( … which our series [a geometric series] is larger [than]

Annuity (2,479 words) [view diff] exact match in snippet view article find links to article

i ) − n 1 − ( 1 + i ) − 1 ) by using the equation for the sum of a geometric series = 1 − ( 1 + i ) − n 1 + i − 1 = 1 − ( 1 1 + i ) n i , {\displaystyle

Jacob Bernoulli (2,179 words) [view diff] exact match in snippet view article find links to article

expression for a geometric series] &c. major est. … si a=b, debebitur plu quam 2½a & minus quam 3a." ( … which our series [a geometric series] is larger [than]

Niche apportionment models (2,102 words) [view diff] case mismatch in snippet view article find links to article

making this model stochastic in nature. A closely related model, the Geometric Series, is a deterministic version of the Dominance pre-emption model, wherein

Betti number (2,508 words) [view diff] exact match in snippet view article find links to article

2 + x 4 + ⋯ {\displaystyle 1+x^{2}+x^{4}+\dotsb } , which, being a geometric series, can be expressed as the rational function 1 1 − x 2 . {\displaystyle

Weyl character formula (3,622 words) [view diff] exact match in snippet view article find links to article

{\sin((m+1)\theta )}{\sin \theta }}.} The character in this case is a geometric series with R = e 2 i θ {\displaystyle R=e^{2i\theta }} and that preceding

Siegel G-function (204 words) [view diff] exact match in snippet view article find links to article

of f grow no faster than a geometric series. Indeed, the functions can be considered as generalisations of geometric series, whence the name G-function

Mittag-Leffler function (1,873 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \alpha =0} , the series above equals the Taylor expansion of the geometric series and consequently E 0 , β ( z ) = 1 Γ ( β ) 1 1 − z {\displaystyle E_{0

1 + 2 + 3 + 4 + ⋯ (4,231 words) [view diff] exact match in snippet view article find links to article

divergent geometric series 1 + 2 + 4 + 8 + ⋯. Euler hints that series of this type have finite, negative sums, and he explains what this means for geometric series

Dividend discount model (1,373 words) [view diff] exact match in snippet view article find links to article

{\displaystyle r'={\frac {(1+g)}{(1+r)}}.} The series in parentheses is the geometric series with common ratio r ′ {\displaystyle r'} so it sums to 1 1 − r ′ {\displaystyle

Multiplier (economics) (1,462 words) [view diff] exact match in snippet view article

in the next period (time t+1), and a constant rate of flow yields geometric series, which computes a multiplier. The modern theory of the multiplier was

Power of two (3,882 words) [view diff] exact match in snippet view article find links to article

which is a perfect number. Book IX, Proposition 35, proves that in a geometric series if the first term is subtracted from the second and last term in the

History of combinatorics (2,071 words) [view diff] exact match in snippet view article find links to article

which dates to the 16th century BCE. The problem concerns a certain geometric series, and has similarities to Fibonacci's problem of counting the number

Sharon Gold (4,694 words) [view diff] no match in snippet view article find links to article

Sharon Gold (born February 28, 1949) is an American artist and associate professor of painting at Syracuse University. Gold's artwork has been installed

Kostant partition function (1,711 words) [view diff] exact match in snippet view article find links to article

{\mathfrak {h}}} , we can formally apply the formula for the sum of a geometric series to obtain 1 1 − e − α ( H ) = 1 + e − α ( H ) + e − 2 α ( H ) + ⋯ {\displaystyle

Liouville–Neumann series (409 words) [view diff] exact match in snippet view article find links to article

kernel for the integral operator) is then given by a schematic analog "geometric series", R ( x , z ; λ ) = ∑ n = 0 ∞ λ n K n ( x , z ) . {\displaystyle R\left(x

List of mathematical proofs (593 words) [view diff] exact match in snippet view article find links to article

sector, basis of hyperbolic angle Infinite series convergence of the geometric series with first term 1 and ratio 1/2 Integer partition Irrational number

Bakhshali manuscript (2,148 words) [view diff] exact match in snippet view article find links to article

equations, quadratic equations, arithmetic progressions and arithmetico-geometric series, computing square roots approximately, dealing with negative numbers

Closed timelike curve (1,924 words) [view diff] exact match in snippet view article find links to article

terminates at a finite value after infinitely many revolutions because the geometric series converges. Causal structure Causality conditions Quantum mechanics

Uniform absolute-convergence (441 words) [view diff] exact match in snippet view article find links to article

and the series Σ|fn(x)| converges absolutely at each point by the geometric series test, but Σ|fn(x)| does not converge uniformly. Intuitively, this is

George Andrews (mathematician) (838 words) [view diff] exact match in snippet view article

Pennsylvania State University, the world authority on partitions and q-geometric series. "University of Illinois commencement ceremony to take place May 17

Hard spheres (892 words) [view diff] exact match in snippet view article find links to article

Starling. By expressing the compressibility of a hard-sphere system as a geometric series, the expression Z = p V n R T = 1 + η + η 2 − η 3 ( 1 − η ) 3 {\displaystyle

Michael Stifel (1,157 words) [view diff] exact match in snippet view article find links to article

points out, that multiplication and division operations in the (lower) geometric series can be mapped by addition and subtraction in the (upper) arithmetic

Kingdom of Tanur (7,353 words) [view diff] exact match in snippet view article find links to article

is now considered the first example of a power series (apart from geometric series). However, they did not formulate a systematic theory of differentiation

Latin letters used in mathematics, science, and engineering (3,835 words) [view diff] exact match in snippet view article find links to article

inradius of a triangle or other tangential polygon the ratio of a geometric series (e.g. arn−1) the separation of two objects, for example in Coulomb's

Roulette (7,447 words) [view diff] exact match in snippet view article find links to article

betting systems are essentially an attempt to beat the fact that a geometric series with initial value of 0.95 (American roulette) or 0.97 (European roulette)

George Pólya Award (121 words) [view diff] case mismatch in snippet view article find links to article

Effect 2006 Ezra (Bud) Brown Phoebe Floats! 2006 James Sandefur A Geometric Series from Tennis 2005 Brian Hopkins and Robin J. Wilson The Truth About

Angle trisection (3,121 words) [view diff] exact match in snippet view article find links to article

of the compass and straightedge method for bisecting an angle. The geometric series 1/3 = 1/4 + 1/16 + 1/64 + 1/256 + ⋯ or 1/3 = 1/2 − 1/4 + 1/8 − 1/16

Evangelista Torricelli (3,062 words) [view diff] exact match in snippet view article find links to article

sequence, and in this way gives a proof of the formula for the sum of a geometric series. Torricelli developed further the method of indivisibles of Cavalieri

Pi (17,361 words) [view diff] exact match in snippet view article find links to article

the fact that the differences in area of successive polygons form a geometric series with a factor of 4. The Chinese mathematician Zu Chongzhi, around 480 AD

Baltimore Type Foundry (537 words) [view diff] case mismatch in snippet view article find links to article

foundry types were originally cast by the first Baltimore Type Foundry: Geometric Series (1884) Oak Leaf (1832) The second Baltimore Type & Composition Co.

Screw (6,078 words) [view diff] exact match in snippet view article find links to article

1 mm pitch. Other threads in the BA series are related to 0BA in a geometric series with the common factors 0.9 and 1.2. For example, a 4BA thread has

König's theorem (complex analysis) (342 words) [view diff] exact match in snippet view article

{\displaystyle f(x)=\sum _{n=0}^{\infty }c_{n}x^{n}} will vary akin to the geometric series and this will also be manifest in the coefficients of f {\displaystyle

Mortgage calculator (2,134 words) [view diff] exact match in snippet view article find links to article

fixed monthly payment c (with x = 1 + r {\displaystyle x=1+r} ) is a geometric series, which has a simple closed-form expression obtained from observing

Preferred number (2,827 words) [view diff] exact match in snippet view article find links to article

types of products. They vary and often deviate significantly from any geometric series in order to accommodate traditional sizes when feasible. Adjacent package

Fourier series (10,850 words) [view diff] exact match in snippet view article find links to article

Fourier series is an extension (the addition of an arm) of the complex geometric series which has just one arm. It also shows how the two arms coordinate with

Runge's theorem (889 words) [view diff] exact match in snippet view article find links to article

_{n=0}^{\infty }\left({\frac {z_{0}-w_{0}}{z-w_{0}}}\right)^{n}} (verified by geometric series) valid on the circle-complement | z 0 − w 0 | < | z − w | {\displaystyle

Compact group (4,472 words) [view diff] exact match in snippet view article find links to article

}+e^{-im\theta }.} (If we use the formula for the sum of a finite geometric series on the above expression and simplify, we obtain the earlier expression

Divergence of the sum of the reciprocals of the primes (2,898 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \{p_{k+1},p_{k+2},\cdots \}} . It follows that the geometric series ∑ i = 0 ∞ ( x k ) i {\textstyle \sum _{i=0}^{\infty }(x_{k})^{i}} contains

History of science and technology on the Indian subcontinent (7,630 words) [view diff] exact match in snippet view article find links to article

is now considered the first example of a power series (apart from geometric series). Mathmatation Narayana Pandit wrote two works, an arithmetical treatise

John Wallis (5,116 words) [view diff] exact match in snippet view article find links to article

thinking: Leonhard Euler came to the same conclusion by considering the geometric series 1 1 − x = 1 + x + x 2 + ⋯ {\displaystyle {\tfrac {1}{1-x}}=1+x+x^{2}+\cdots

Lagrange inversion theorem (2,833 words) [view diff] exact match in snippet view article find links to article

i}}\oint _{C}{\frac {\omega }{f(\omega )-z}}f'(\omega )d\omega } using geometric series: 1 f ( ω ) − z = 1 f ( ω ) − f ( a ) − z + f ( a ) = 1 f ( ω ) − f

Sakuma–Hattori equation (1,175 words) [view diff] exact match in snippet view article find links to article

standard numerical treatment expands the incomplete integral in a geometric series of the exponential ∫ 0 λ 2 c 1 λ 5 [ exp ⁡ ( c 2 λ T ) − 1 ] d λ =

Fundamental theorem of algebra (7,721 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \int _{c(r)}R(z)\,dz=0.} On the other hand, R(z) expanded as a geometric series gives: R ( z ) = z − 1 ( I n − z − 1 A ) − 1 = z − 1 ∑ k = 0 ∞ 1 z

Jama Musse Jama (686 words) [view diff] exact match in snippet view article find links to article

other animals, as etnomathematical illustration of the mathematical geometric series of 0.5 = 1.0. Xarunta Dhaqanka ee Hargeysa (Hargeysa Cultural Centre)

Representation theory of SU(2) (3,397 words) [view diff] exact match in snippet view article

}+\cdots +e^{-i(m-2)\theta }+e^{-im\theta }.} This expression is a finite geometric series that can be simplified to X ( ( e i θ 0 0 e − i θ ) ) = sin ⁡ ( ( m

Molien's formula (1,307 words) [view diff] exact match in snippet view article find links to article

{1}{(1-t)(1-t^{2})(1-t^{3})}}.} On the other hand, we can expand the geometric series and multiply out to get M ( t ) = ( 1 + t + t 2 + t 3 + ⋯ ) ( 1 + t

Science in classical antiquity (6,342 words) [view diff] exact match in snippet view article find links to article

communicated many remarkable results, such as the sum of an infinite geometric series in Quadrature of the Parabola, an approximation to the value π in Measurement

List of sums of reciprocals (2,133 words) [view diff] exact match in snippet view article find links to article

2 . This is a particular case of the sum of the reciprocals of any geometric series where the first term and the common ratio are positive integers. If

Education in Kerala (9,499 words) [view diff] exact match in snippet view article find links to article

is now considered the first example of a power series (apart from geometric series). However, they did not formulate a systematic theory of differentiation

Timeline of scientific discoveries (10,204 words) [view diff] exact match in snippet view article find links to article

the sizes of images. 3rd century BC: Archimedes relates problems in geometric series to those in arithmetic series, foreshadowing the logarithm. 3rd century

Stencil buffer (2,390 words) [view diff] exact match in snippet view article find links to article

shadow, and that as the copies, respectively are scaled according to a geometric series with a low magnification, e.g.,. 1.04. The Center of scaling can be

List of eponymous laws (10,163 words) [view diff] exact match in snippet view article find links to article

Dermott's law: The sidereal period of major satellites tends to follow a geometric series. Named after Stanley Dermott. De Vaucouleurs' law, in astronomy, describes

Stencil buffer (2,390 words) [view diff] exact match in snippet view article find links to article

shadow, and that as the copies, respectively are scaled according to a geometric series with a low magnification, e.g.,. 1.04. The Center of scaling can be

List of Indian inventions and discoveries (21,759 words) [view diff] exact match in snippet view article find links to article

is now considered the first example of a power series (apart from geometric series). However, they did not formulate a systematic theory of differentiation

Scherrer equation (3,254 words) [view diff] exact match in snippet view article find links to article

^{-iqak}\times \sum _{j=1}^{N}\mathrm {e} ^{iqaj}} each sum is a simple geometric series, defining y = exp ⁡ ( i q a ) {\displaystyle y=\exp(iqa)} , ∑ j = 1

Structure factor (7,575 words) [view diff] exact match in snippet view article find links to article

demonstrated with a 1-D lattice of points. The sum of the phase factors is a geometric series and the structure factor becomes: S ( q ) = 1 N | 1 − e − i N q a 1

Partial fractions in complex analysis (2,604 words) [view diff] exact match in snippet view article find links to article

{-8z}{4z^{2}-(2k+1)^{2}\pi ^{2}}}.} We can expand the summand using a geometric series: − 8 z 4 z 2 − ( 2 k + 1 ) 2 π 2 = 8 z ( 2 k + 1 ) 2 π 2 1 1 − ( 2

Noncommutative signal-flow graph (1,660 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \lambda } is the empty word. The similarity to the infinite geometric series ( 1 − x ) − 1 = 1 + x + x 2 + x 3 ⋯ , {\displaystyle (1-x)^{-1}=1+x+x^{2}+x^{3}\cdots

Diffuse reflectance spectroscopy (5,354 words) [view diff] exact match in snippet view article find links to article

problem of some interest". He solved the problem using summations of geometric series, but the results are expressed as continuous functions. This means

Average order of an arithmetic function (4,020 words) [view diff] exact match in snippet view article find links to article

_{n=0}^{\infty }b_{n}u^{n}.} Finally, expand the left-hand side in a geometric series and compare the coefficients on u n {\displaystyle u^{n}} on both sides

Continuous-repayment mortgage (5,497 words) [view diff] exact match in snippet view article find links to article

t\end{aligned}}} It can already be seen that the terms containing MN form a geometric series with common ratio 1 + rΔ t. This enables us to write a general expression

Incoherent broad-band cavity-enhanced absorption spectroscopy (3,720 words) [view diff] exact match in snippet view article find links to article

superposition of the light after an odd number of passes, leading to a geometric series: I = I i n ( 1 − R ) 2 ( 1 − L ) ∑ n = 0 ∞ R 2 n ( 1 − L ) 2 n {\displaystyle

Harry van Kuyk (1,943 words) [view diff] exact match in snippet view article find links to article

Schoonhoven and Shlomo Koren created their own embossed versions of white, geometric series. In 1971, van Kuyk, supported by substantial state financial funding

Chen Shu-ming (1,131 words) [view diff] exact match in snippet view article find links to article

and elegance, and is ethereal and clean. The other is the abstract geometric series of paintings, in which geometric color blocks are arranged and combined

Volume and displacement indicators for an architectural structure (4,259 words) [view diff] exact match in snippet view article find links to article

kn+1 = (c + 1) kn or kn+1 = (c+1)n k0. This is the principle of the geometric series known as the Renard Series (named after Colonel Renard who was the