Hypergeometric Gevrey-0 approximation for the Gevrey-<i>k </i>divergent series with application to eight-loop renormalization group functions of the O(<i>N</i>)-symmetric field model
<p dir="ltr">Mera et al. (Phys Rev Lett 115:143001, 2015) discovered that the hypergeometric function can serve as an accurate approximant for a divergent Gevrey-1 type of series with an asymptotic large-order behavior of the form . What is strange about this approximant is that it h...
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2024
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| Summary: | <p dir="ltr">Mera et al. (Phys Rev Lett 115:143001, 2015) discovered that the hypergeometric function can serve as an accurate approximant for a divergent Gevrey-1 type of series with an asymptotic large-order behavior of the form . What is strange about this approximant is that it has a series expansion with the wrong large-order behavior (Gevrey-0 type). In this work, we extend this discovery to Gevrey-k series where we show that the hypergeometric approximants and its extension to the generalized hypergeometric approximants are not only able to approximate divergent (Gevrey-1) series but also able to approximate strongly-divergent series of Gevrey-k type with . Moreover, we show that these hypergeometric approximants are able to predict accurate results for the non-perturbative strong-coupling and large-order parameters from weak-coupling data as input. Examples studied here are the ground-state energy for the anharmonic oscillators. The hypergeometric approximants are also used to approximate the recent eight-loop series (g-expansion) of the renormalization group functions for the O(N)-symmetric scalar field model. Form these functions for , and 3, critical exponents are extracted which are very competitive to results from more sophisticated approximation techniques.</p><h2>Other Information</h2><p dir="ltr">Published in: The European Physical Journal Plus<br>License: <a href="https://creativecommons.org/licenses/by/4.0" target="_blank">https://creativecommons.org/licenses/by/4.0</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1140/epjp/s13360-024-05373-y" target="_blank">https://dx.doi.org/10.1140/epjp/s13360-024-05373-y</a></p> |
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