Error bounds for the large-argument asymptotic expansions of the Hankel and Bessel functions

In this paper, we reconsider the large-argument asymptotic expansions of the Hankel, Bessel and modified Bessel functions and their derivatives. New integral representations for the remainder terms of these asymptotic expansions are found and used to obtain sharp and realistic error bounds. We also give re-expansions for these remainder terms and provide their error estimates. A detailed discussion on the sharpness of our error bounds and their relation to other results in the literature is given. The techniques used in this paper should also generalize to asymptotic expansions which arise from an application of the method of steepest descents.Comment: 32 pages, 2 figures, accepted for publication in Acta Applicandae Mathematica

The Effectiveness of Family Constellation Therapy in Improving Mental Health:A Systematic ReviewPalabras clave(sic)(sic)(sic)

Family/systemic constellation therapy is a short-term group intervention aiming to help clients better understand and then change their conflictive experiences within a social system (e.g., family). The aim of the present systematic review was to synthetize the empirical evidence on the tolerability and effectiveness of this intervention in improving mental health. The PsycINFO, Embase, MEDLINE, ISI Web of Science, Psyndex, PsycEXTRA, ProQuest Dissertations & Theses, The Cochrane Library, Google Scholar, and an intervention-specific organization's databases were searched for quantitative, prospective studies published in English, German, Spanish, French, Dutch or Hungarian up until April 2020. Out of 4,197 identified records, 67 were assessed for eligibility, with 12 studies fulfilling inclusion criteria (10 independent samples; altogether 568 participants). Outcome variables were diverse ranging from positive self-image through psychopathology to perceived quality of family relationships. Out of the 12 studies, nine showed statistically significant improvement postintervention. The studies showing no significant treatment benefit were of lower methodological quality. The random-effect meta-analysis-conducted on five studies in relation to general psychopathology-indicated a moderate effect (Hedges' g of 0.531, CI: 0.387-0.676). Authors of seven studies also investigated potential iatrogenic effects and four studies reported minor or moderate negative effects in a small proportion (5-8%) of participants that potentially could have been linked to the intervention. The data accumulated to date point into the direction that family constellation therapy is an effective intervention with significant mental health benefits in the general population; however, the quantity and overall quality of the evidence is low