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  • Estimating the sequence of real binomial coefficients [Elektronski vir]
    Lampret, Vito
    The sequence ▫$n \mapsto {a \choose n}$▫ of real binomial coefficients is studied in two main cases: ▫$a \gg n$▫ and ▫$n \gg a$▫. In the first case a uniform approximation with high accuracy is ... obtained, in contrast to DeMoivre-Laplace approximation, which has essentially local character and is good only for ▫$n \approx \frac{a}{2}$▫. In the second case, for every ▫$a \in \mathbb R \setminus (\mathbb N \cup \{-1,0\})$▫, the functions ▫$A(a,m)$▫ and ▫$B(a,m)$▫ are determined, such that ▫$\lim_{m \to \infty} \frac{A(a,m)}{B(a,m)} = 1$▫, and ▫$$A(a,m) \cdot (n-a)^{-(a+1)} < \left| {a \choose n} \right| < B(a,m) \cdot (n-a)^{-(n+1)},$$▫ for integers ▫$m$▫ and ▫$n$▫, obeying ▫$n > m > |a|$▫.
    Source: Journal of inequalities in pure and applied mathematics [Elektronski vir]. - ISSN 1443-5756 (Vol. 7, iss. 5, 2006, art. 166 (16 str.))
    Type of material - e-article
    Publish date - 2006
    Language - english
    COBISS.SI-ID - 14231129

    Link(s):

    http://www.emis.de/journals/JIPAM/article784.html?sid=784

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