Abstract
The Euler–Frobenius polynomials have been throughout the book to characterize asymptotic sampling zeros in discrete models as the sampling period goes to zero. This chapter presents a brief historical account of these polynomials, and a summary of (equivalent) definitions and properties found in the literature.
Contributed by Diego S. Carrasco School of Electrical Engineering and Computer Science The University of Newcastle, Australia
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Further Reading
Material on generating functions can be found in
Wilf HS (2005) Generatingfunctionology, 3rd edn. CRC Press, Boca Raton
Material on combinatorial analysis and Euler, Bernoulli, and Eulerian polynomials and numbers can be found in
Comtet L (1974) Advanced combinatorics: the art of finite and infinite expansions. Reidel, Dordrecht
Graham RL, Knuth DE, Patashnik O (1994) Concrete mathematics, 2nd edn. Addison-Wesley, Reading
Olver FWJ, Lozier DW, Boisvert RF, Clark CW (eds) (2010) NIST handbook of mathematical functions. Cambridge University Press, New York. Print companion to http://dlmf.nist.gov/
Riordan J (1958) Introduction to combinatorial analysis. Wiley, New York
Euler’s work and a glimpse into his life can be found in
Euler L (1755) Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum. Available online: http://eulerarchive.maa.org/pages/E212.html
Euler L (1768) Remarques sur un beau rapport entre les series des puissances tant directes que reciproques. Mem Acad Sci Berl 17:83–106. Available online: http://eulerarchive.maa.org/pages/E352.html
Gautschi W (2008) Leonhard Euler: his life, the man, and his works. SIAM Rev 50(1):3–33
Extensive material on Eulerian/Euler–Frobenius polynomials can be found in
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Yuz, J.I., Goodwin, G.C. (2014). The Euler–Frobenius Polynomials. In: Sampled-Data Models for Linear and Nonlinear Systems. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-5562-1_20
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