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17 relations: Abel's summation formula, Abelian and tauberian theorems, Algebraic curve, Binomial series, Coefficient, Divergent series, Generating function, Limit (mathematics), Mathematics, Nachbin's theorem, Niels Henrik Abel, One-sided limit, Power series, Probability-generating function, Radius of convergence, Sequence, Summation by parts.
Abel's summation formula
In mathematics, Abel's summation formula, introduced by Niels Henrik Abel, is intensively used in number theory to compute series.
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Abelian and tauberian theorems
In mathematics, Abelian and Tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named after Niels Henrik Abel and Alfred Tauber.
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Algebraic curve
In mathematics, a plane real algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables.
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Binomial series
In mathematics, the binomial series is the Maclaurin series for the function f given by f(x).
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Coefficient
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but may be any expression.
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Divergent series
In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.
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Generating function
In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.
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Limit (mathematics)
In mathematics, a limit is the value that a function (or sequence) "approaches" as the input (or index) "approaches" some value.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Nachbin's theorem
In mathematics, in the area of complex analysis, Nachbin's theorem (named after Leopoldo Nachbin) is commonly used to establish a bound on the growth rates for an analytic function.
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Niels Henrik Abel
Niels Henrik Abel (5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields.
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One-sided limit
In calculus, a one-sided limit is either of the two limits of a function f(x) of a real variable x as x approaches a specified point either from below or from above.
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Power series
In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.
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Probability-generating function
In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable.
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Radius of convergence
In mathematics, the radius of convergence of a power series is the radius of the largest disk in which the series converges.
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Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
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Summation by parts
In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums.
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