caa a22 4500 605466297 CHVBK 20210128100306.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s00397-014-0802-2 doi (NATIONALLICENCE)springer-10.1007/s00397-014-0802-2 Jedynak Radosław Kazimierz Pulaski University of Technology and Humanities, ul. Malczewskiego 20a, 26-600, Radom, Poland aut Approximation of the inverse Langevin function revisited [Elektronische Daten] [Radosław Jedynak] The main purpose of this paper is to provide an easy-to-use approximation formula for the inverse Langevin function. The mathematical complexity of this function makes it unfeasible for an analytical manipulation and inconvenient for computer simulation. This situation has motivated a series of papers directed on its approximation. The best known solution is given by Cohen. It is used in a lot of statistically based models of rubber-like materials. The formula is derived from rounded Padé approximation [3/2]. The main idea of the presented approach in this paper relies on improvement of the precision of approximation formula for the inverse Langevin function by using multipoint Padé approximation method. We focused our study strongly on obtaining a simple and accurate approximation. It is assumed that the proposed approximation formula may be considered a useful tool for verification of the results obtained in other ways. Our results are supported by investigating several numerical examples. The paper also presents a few applications of computer software named Mathematica which can be used to calculate symbolically one point Padé approximants and numerically multipoint Padé approximants. Using this software, we showed also how to compute higher order derivatives of the inverse function in a simple and elegant way. This issue was discussed by Itskov et al. The Author(s), 2014 Inverse Langevin function nationallicence Padé approximation nationallicence Non-Gaussian statistics nationallicence Taylor expansion nationallicence Mathematica computer software nationallicence Rheologica Acta Springer Berlin Heidelberg 54/1(2015-01-01), 29-39 0035-4511 54:1<29 2015 54 397 https://doi.org/10.1007/s00397-014-0802-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00397-014-0802-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Jedynak Radosław Kazimierz Pulaski University of Technology and Humanities, ul. Malczewskiego 20a, 26-600, Radom, Poland aut NATIONALLICENCE 773 0- Rheologica Acta Springer Berlin Heidelberg 54/1(2015-01-01), 29-39 0035-4511 54:1<29 2015 54 397