Mashreghi–Ransford inequality

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In Mathematics, the Mashreghi–Ransford inequality is a bound on the growth rate of certain sequences. It is named after J. Mashreghi and T. Ransford.

Mathematics Field of study concerning quantity, patterns and change

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Thomas Ransford Ph.D. Sc.D is a British-born Canadian mathematician, known for his research in spectral theory and complex analysis. He holds a Canada Research Chair in mathematics at Université Laval.

Let be a sequence of complex numbers, and let

Complex number Element of a number system in which –1 has a square root

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. Because no real number satisfies this equation, i is called an imaginary number. For the complex number a + bi, a is called the real part, and b is called the imaginary part. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers, and are fundamental in many aspects of the scientific description of the natural world.

and

We remind that the binomial coefficients are defined by

Assume that, for some , we have and as . Then

, as ,

where

Moreover, there is a universal constant such that

The precise value of is unknown. However, it is known that

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