Browse > Article
http://dx.doi.org/10.14317/jami.2021.541

EXPLICIT PROPERTIES OF q-SIGMOID POLYNOMIALS COMBINING q-COSINE FUNCTION  

KANG, JUNG YOOG (Department of Mathematics Education, Silla University)
Publication Information
Journal of applied mathematics & informatics / v.39, no.3_4, 2021 , pp. 541-552 More about this Journal
Abstract
In this paper, we introduce q-sigmoid polynomials combining q-cosine function. We find several properties and identities of these polynomials which are related to sigmoid function using deep learning.
Keywords
Sigmoid function; q-cosine sigmoid polynomials; q-cosine Bernoulli polynomials;
Citations & Related Records
연도 인용수 순위
  • Reference
1 H. Exton, q-Hypergeometric Functions and Applications, New York: Halstead Press, Chichester: Ellis Horwood, 1983.
2 J. Han, C. Moraga, The influence of the sigmoid function parameters on the speed of backpropagation learning, International Workshop on Artificial Neural Networks doi: https://doi.org/10.1007/3-540-59497-3175.
3 J. Han, R.S. Wilson, S.E. Leurgans, Sigmoidal mixed models for longitudinal data, Statistical Methods in Medical Research doi: https://doi.org/10.1177/0962280216645632.
4 Y. Ito, Representation of functions by superpositions of a step or sigmoid function and their applications to neural network theory, Neural Networks 4 (1991), 385-394.   DOI
5 H.K. Kwan, Simple sigmoid-like activation function suitable for digital hardware implementation, Electronics Letters 28 (1992), doi: 10.1049/el:19920877   DOI
6 H.F. Jackson, q-Difference equations, Am. J. Math. 32 (1910), 305-314.   DOI
7 V. Kac, P. Cheung, Quantum Calculus, Universitext, Springer-Verlag, 2002.
8 T. Kim, C.S. Ryoo, Some identities for Euler and Bernoulli polynomials and their zeros, Axioms 7 (2018), 1-19.   DOI
9 J.Y. Kang, C.S. Ryoo, Various structures of the roots and explicit properties of q-cosine Bernoulli Polynomials and q-sine Bernoulli Polynomials, Mathematics 8 (2020), 1-18.   DOI
10 J.Y. Kang, Some relationships between sigmoid polynomials and other polynomials, J. Appl. & Pure Math. 1 (2019), 57-67.
11 J.Y. Kang, Some Properties and Distribution of the Zeros of the q-Sigmoid Polynomials, Discrete Dynamics in Nature and Society 2020 (2020), 1-10.