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Note on an inequality for the coefficients in legendre polynomial expansions and its application to the theory of liquid phase transitions

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Abstract

It is shown that if themth derivative of a function is positive, and it has a Legendre polynomial expansion with coefficients,A n, then (A m)/(2m+1)≧(A n)/(2n+1) forn>m. This result is applied to the theory of liquid phase transitions.

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Literature

  • Isenberg, I. 1954. “On the Theory of the Nematic Phase and Its Possible Relation to the Mitotic Spindle Structure.”Bull Math. Biophysics,16, 83–96.

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  • Szegö, G. 1939.Orthogonal Polynomials. New York: American Mathematical Society.

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  • Zimmer, L. T. 1955. “Some Possible Phase Transitions in Dilute Colloidal Solutions.”Bull. Math. Biophysics,17, 51–61.

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Authors and Affiliations

  1. Illinois Institute of Technology, Chicago, Illinois

    H. G. Landau

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  1. H. G. Landau
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Landau, H.G. Note on an inequality for the coefficients in legendre polynomial expansions and its application to the theory of liquid phase transitions. Bulletin of Mathematical Biophysics 17, 41–44 (1955). https://doi.org/10.1007/BF02481836

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  • DOI: https://doi.org/10.1007/BF02481836

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