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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| _version_ | 1864513541540675584 |
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| author | Abouzeid M. Shalaby (16810695) |
| author2 | Hamdi M. Abdelhamid (16810692) I. S. Elkamash (22046441) |
| author2_role | author author |
| author_facet | Abouzeid M. Shalaby (16810695) Hamdi M. Abdelhamid (16810692) I. S. Elkamash (22046441) |
| author_role | author |
| dc.creator.none.fl_str_mv | Abouzeid M. Shalaby (16810695) Hamdi M. Abdelhamid (16810692) I. S. Elkamash (22046441) |
| dc.date.none.fl_str_mv | 2024-07-07T03:00:00Z |
| dc.identifier.none.fl_str_mv | 10.1140/epjp/s13360-024-05373-y |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/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/29899577 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Mathematical sciences Mathematical physics Hypergeometric approximants Gevrey series Divergent series resummation Asymptotic analysis Perturbation theory Anharmonic oscillator |
| dc.title.none.fl_str_mv | 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 |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <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> |
| eu_rights_str_mv | openAccess |
| id | Manara2_682dbfa2bad71b6f9fc17075a54e9394 |
| identifier_str_mv | 10.1140/epjp/s13360-024-05373-y |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/29899577 |
| publishDate | 2024 |
| repository.mail.fl_str_mv | |
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| rights_invalid_str_mv | CC BY 4.0 |
| spelling | 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 modelAbouzeid M. Shalaby (16810695)Hamdi M. Abdelhamid (16810692)I. S. Elkamash (22046441)Mathematical sciencesMathematical physicsHypergeometric approximantsGevrey seriesDivergent series resummationAsymptotic analysisPerturbation theoryAnharmonic oscillator<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>2024-07-07T03:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.1140/epjp/s13360-024-05373-yhttps://figshare.com/articles/journal_contribution/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/29899577CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/298995772024-07-07T03:00:00Z |
| spellingShingle | 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 Abouzeid M. Shalaby (16810695) Mathematical sciences Mathematical physics Hypergeometric approximants Gevrey series Divergent series resummation Asymptotic analysis Perturbation theory Anharmonic oscillator |
| status_str | publishedVersion |
| title | 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 |
| title_full | 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 |
| title_fullStr | 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 |
| title_full_unstemmed | 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 |
| title_short | 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 |
| title_sort | 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 |
| topic | Mathematical sciences Mathematical physics Hypergeometric approximants Gevrey series Divergent series resummation Asymptotic analysis Perturbation theory Anharmonic oscillator |