<abstract xmlns="http://www.w3.org/1999/xhtml">There is no mathematical solution to adding up transcendental functions other than numerical process. This paper put forward analytical method to model the sum of sigmoid like functions with an equivalent function. The <italic>Brillouin</italic> and <italic>Langevin</italic> as well as the <italic>error</italic> function, the <italic>tanh</italic>, <italic>sigmoid</italic> and the <italic>tan-</italic>1 functions are investigated, their equivalent functions are calculated for four components and the error between the numerical (computer assisted) result and the equivalent function is tested for accuracy. The best modelling function, the most useful to include into mathematical operations, is pointed out finally, based on its performance and convenience. The paper intends to help people involved mostly in modelling hysteresis in Magnetism and other field of research in physics.</abstract>

There is no mathematical solution to adding up transcendental functions other than numerical process. This paper put forward analytical method to model the sum of sigmoid like functions with an equivalent function. The Brillouin and Langevin as well as the error function, the tanh, sigmoid and the tan-1 functions are investigated, their equivalent functions are calculated for four components and the error between the numerical (computer assisted) result and the equivalent function is tested for accuracy. The best modelling function, the most useful to include into mathematical operations, is pointed out finally, based on its performance and convenience. The paper intends to help people involved mostly in modelling hysteresis in Magnetism and other field of research in physics.

Equivalent Analytical Functions of Sums of Sigmoid like Transcendental Functions

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Equivalent Analytical Functions of Sums of Sigmoid like Transcendental Functions"}

There is no mathematical solution to adding up transcendental functions other than numerical process. This paper put forward analytical method to model the sum...

Equivalent Analytical Functions of Sums of Sigmoid like Transcendental Functions

Published Online: Jul 19, 2018

Page range: 403 - 408

Received: Mar 03, 2018

Accepted: Jul 19, 2018

DOI: https://doi.org/10.21042/AMNS.2018.2.00030

Keywords
transcendental functions, sigmoid functions, modelling

© 2018 J. Takács, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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Equivalent Analytical Functions of Sums of Sigmoid like Transcendental Functions

Published Online: Jul 19, 2018

Page range: 403 - 408

Received: Mar 03, 2018

Accepted: Jul 19, 2018

DOI: https://doi.org/10.21042/AMNS.2018.2.00030

Keywordstranscendental functions, sigmoid functions, modelling

© 2018 J. Takács, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Fig. 3

Keywords
transcendental functions, sigmoid functions, modelling