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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.

Let be a sequence of complex numbers, and let

and

Here the binomial coefficients are defined by

Assume that, for some , we have and as . Then Mashreghi-Ransford showed that

, as ,

where Moreover, there is a universal constant such that

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

References

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  • Mashreghi, J.; Ransford, T. (2005). "Binomial sums and functions of exponential type". Bull. London Math. Soc. 37 (1): 15–24. doi:10.1112/S0024609304003625. S2CID 122766740..