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  2. Convergence tests - Wikipedia

    en.wikipedia.org/wiki/Convergence_tests

    Raabe–Duhamel's test. Let { an } be a sequence of positive numbers. Define. If. exists there are three possibilities: if L > 1 the series converges (this includes the case L = ∞) if L < 1 the series diverges. and if L = 1 the test is inconclusive. An alternative formulation of this test is as follows.

  3. Cauchy's convergence test - Wikipedia

    en.wikipedia.org/wiki/Cauchy's_convergence_test

    Cauchy's convergence test. The Cauchy convergence test is a method used to test infinite series for convergence. It relies on bounding sums of terms in the series. This convergence criterion is named after Augustin-Louis Cauchy who published it in his textbook Cours d'Analyse 1821. [1]

  4. Convergence of random variables - Wikipedia

    en.wikipedia.org/wiki/Convergence_of_random...

    Definition. A sequence of real-valued random variables, with cumulative distribution functions , is said to converge in distribution, or converge weakly, or converge in law to a random variable X with cumulative distribution function F if. for every number at which F is continuous .

  5. Weierstrass M-test - Wikipedia

    en.wikipedia.org/wiki/Weierstrass_M-test

    Weierstrass M-test. In mathematics, the Weierstrass M-test is a test for determining whether an infinite series of functions converges uniformly and absolutely. It applies to series whose terms are bounded functions with real or complex values, and is analogous to the comparison test for determining the convergence of series of real or complex ...

  6. Alternating series - Wikipedia

    en.wikipedia.org/wiki/Alternating_series

    Calculus. In mathematics, an alternating series is an infinite series of the form or with an > 0 for all n. The signs of the general terms alternate between positive and negative. Like any series, an alternating series converges if and only if the associated sequence of partial sums converges .

  7. Dirichlet's test - Wikipedia

    en.wikipedia.org/wiki/Dirichlet's_test

    In mathematics, Dirichlet's test is a method of testing for the convergence of a series. It is named after its author Peter Gustav Lejeune Dirichlet , and was published posthumously in the Journal de Mathématiques Pures et Appliquées in 1862.

  8. Iterative method - Wikipedia

    en.wikipedia.org/wiki/Iterative_method

    Iterative method. In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the i -th approximation (called an "iterate") is derived from the previous ones. A specific implementation with termination ...

  9. Automatic test pattern generation - Wikipedia

    en.wikipedia.org/wiki/Automatic_test_pattern...

    Automatic test pattern generation. ATPG (acronym for both automatic test pattern generation and automatic test pattern generator) is an electronic design automation method or technology used to find an input (or test) sequence that, when applied to a digital circuit, enables automatic test equipment to distinguish between the correct circuit ...

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