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Keywords:
$q$-binomial coefficients
$q$-binomial coefficients
Summary:
In this note, we estimate the distance between two $q$-nomial coefficients $\bigl \lvert \binom {n}{k}_q-\binom {n'}{k'}_q\bigr \rvert $, where $(n,k)\ne (n',k')$ and $q\ge 2$ is an integer.
References:
[1] Luca, F., Marques, D., Stănică , P.: On the spacings between $C$-nomial coefficients. J. Number Theory, 130, 2010, 82-100, DOI 10.1016/j.jnt.2009.07.015 | MR 2569843
[2] Rosser, J. B., Schoenfeld, L.: Approximate formulas for some functions of prime numbers. Illinois J. Math., 6, 1962, 64-94, DOI 10.1215/ijm/1255631807
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