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15 papers · 1 filter
High-Order Parametrization of the Hypergeometric-Meijer Approximants
Abouzeid M. Shalaby
In previous articles, we showed that, based on large-order asymptotic behavior, one can approximate a divergent series via the parametrization of a specific hypergeometric approxim…
The -point anomaly in view of the seven-loop Hypergeometric resummation for the critical exponent of the model
Abouzeid M. Shalaby
In this work, we use a specific parameterization of the hypergeometric approximants ( the one by Mera et.al in Phys. Rev. Let. 115, 143001 (2015)) to approximate the seven-loop cri…
Critical Exponents of the O(N)-symmetric Model from the \boldmath{\large{ }} Hypergeometric-Meijer Resummation
Abouzeid M. Shalaby
We extract the -expansion from the recently obtained seven-loop -expansion for the renormalization group functions of the -symmetric model. The different seri…
Precise Critical Exponents of the O(N)-Symmetric Quantum field Model using Hypergeometric-Meijer Resummation
Abouzeid M. Shalaby
In this work, we show that one can select different types of Hypergeometric approximants for the resummation of divergent series with different large-order growth factors. Being of…
Weak-Coupling, Strong-Coupling and Large-Order Parametrization of the Hypergeometric-Meijer Approximants
Abouzeid M. Shalaby
Without Borel or Pad techniques, we show that for a divergent series with large-order growth factor, the set of Hypergeometric series represents sui…
Extrapolating the precision of the Hypergeometric Resummation to Strong couplings with application to the Symmetric Field Theory
Abouzeid M. Shalaby
In PRL 115, 143001 (2015), H. Mera et al. developed a new simple but precise Hypergeometric Resummation technique. In this work, we suggest to obtain half of the parameters of the…