Abstract
Using known entropic and information inequalities, we obtain new inequalities for some classical polynomials. We consider examples of Jacobi and Legendre polynomials.
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N. Ja. Vilenkin and A. U. Klimyk, Representation of Lie Groups and Special Functions: Recent Advances (Mathematics and Its Applications), Springer (1994).
A. Ibort, V. I. Man’ko, G. Marmo, et al., Phys. Scr., 79, (2009).
M. A. Man’ko, V. I. Man’ko, G. Marmo, et al., Nuovo Cimento C, 36, Ser. 3, 163 (2013).
A. Mandilara, E. Karpov, and N. J. Cerf, J. Phys. A: Math. Theor, 47, 045302 (2014).
C. E. Shannon, Bell Syst. Tech. J., 27, 379 (1948).
R. B. Nelsen, An Introduction to Copulas, Springer (2006).
E. H. Lieb and M. B. Ruskai, J. Math. Phys., 14, 1938 (1973).
E. H. Lieb and R. Seiringer, Phys. Ref. A, 71, 062329 (2005).
V. V. Dodonov and V. I. Man’ko, Invariants and the Evolution of Nonstationary Quantum Systems, Proceedings of the P. N. Lebedev Physical Institute, Nauka, Moscow, Vol. 183 (1987) [English translation: Nova Science, Commack, New York (1989)].
M. A. Man’ko and V. I. Man’ko, Found. Phys., 41, 330 (2011).
M. A. Man’ko and V. I. Man’ko, Phys. Scr., T160, 014030 (2014).
V. N. Chernega and O. V. Man’ko, J. Russ. Laser Res., 35, 27 (2014).
V. N. Chernega and V. I. Man’ko, J. Russ. Laser Res., 29, 505 (2008).
M. A. Man’ko, V. I. Man’ko, and R. Vilela Mendes, J. Russ. Laser Res., 27, 507 (2006).
L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, Butterworth-Heinemann (1977).
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Man’ko, V.I., Markovich, L.A. Entropic Inequalities and Properties of Some Special Functions. J Russ Laser Res 35, 200–210 (2014). https://doi.org/10.1007/s10946-014-9414-7
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DOI: https://doi.org/10.1007/s10946-014-9414-7