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essentially convergent series

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  • Summation of Grandi's series — General considerationstability and linearityThe formal manipulations that lead to 1 − 1 + 1 − 1 + · · · being assigned a value of 1⁄2 include: *Adding or subtracting two series term by term, *Multiplying through by a scalar term by term, *… …   Wikipedia

  • Fourier series — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms …   Wikipedia

  • History of Grandi's series — Geometry and infinite zerosGrandiGuido Grandi (1671 – 1742) reportedly provided a simplistic account of the series in 1703. He noticed that inserting parentheses into nowrap|1=1 − 1 + 1 − 1 + · · · produced varying results: either:(1 1) + (1 1) + …   Wikipedia

  • Absolute convergence — In mathematics, a series (or sometimes also an integral) of numbers is said to converge absolutely if the sum (or integral) of the absolute value of the summand or integrand is finite. More precisely, a real or complex series is said to converge… …   Wikipedia

  • Zeno's paradoxes — Achilles and the Tortoise redirects here. For other uses, see Achilles and the Tortoise (disambiguation). Arrow paradox redirects here. For other uses, see Arrow paradox (disambiguation). Zeno s paradoxes are a set of problems generally thought… …   Wikipedia

  • Stirling's approximation — In mathematics, Stirling s approximation (or Stirling s formula) is an approximation for large factorials. It is named in honour of James Stirling.The formula is written as:n! approx sqrt{2pi n}, left(frac{n}{e} ight)^{n}.Roughly, this means that …   Wikipedia

  • List of real analysis topics — This is a list of articles that are considered real analysis topics. Contents 1 General topics 1.1 Limits 1.2 Sequences and Series 1.2.1 Summation Methods …   Wikipedia

  • philosophy, Western — Introduction       history of Western philosophy from its development among the ancient Greeks to the present.       This article has three basic purposes: (1) to provide an overview of the history of philosophy in the West, (2) to relate… …   Universalium

  • Gauss's continued fraction — In complex analysis, Gauss s continued fraction is a particular class of continued fractions derived from hypergeometric functions. It was one of the first analytic continued fractions known to mathematics, and it can be used to represent several …   Wikipedia

  • Bessel-Clifford function — In mathematical analysis, the Bessel Clifford function is an entire function of two complex variables which can be used to provide an alternative development of the theory of Bessel functions. If :pi(x) = frac{1}{Pi(x)} = frac{1}{Gamma(x+1)}is… …   Wikipedia

  • The Mote in God's Eye —   …   Wikipedia


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