Abstract
In this paper some computational aspects of studying various properties of multiple orthogonal polynomials are presented. The results were obtained using the symbolic and numerical computations in Mathematica (www.wolfram.com). This paper is mainly based on papers Filipuk et al., J Phys A: Math Theor 46:205–204, 2013, [1], Van Assche et al., J Approx Theory 190:1–25, 2015, [2], Zhang and Filipuk, Symmetry Integr Geom Methods Appl 10:103, 2014, [3] (joint with W. Van Assche and L. Zhang). We also perform the Painlevé analysis of certain nonlinear differential equation related to multiple Hermite polynomials and show the existence of two types of polar expansions, which might be useful to obtain relations for zeros of these polynomials.
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References
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Acknowledgments
The author is grateful to the organizers of the conference Modern Mathematical Methods and High Performance Computing in Science and Technology for their invitation and the opportunity to record a video lecture.
This paper is an extension of the video lecture. The author also acknowledges the support of the Alexander von Humboldt Foundation and the hospitality of the Catholic University Eichstätt-Ingolstadt.
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Filipuk, G. (2016). The Properties of Multiple Orthogonal Polynomials with Mathematica. In: Singh, V., Srivastava, H., Venturino, E., Resch, M., Gupta, V. (eds) Modern Mathematical Methods and High Performance Computing in Science and Technology. Springer Proceedings in Mathematics & Statistics, vol 171. Springer, Singapore. https://doi.org/10.1007/978-981-10-1454-3_8
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DOI: https://doi.org/10.1007/978-981-10-1454-3_8
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