A representation formula of sum rules for zeros of polynomials

  • Paolo Emilio Ricci


A representation formula in terms of Lucas polynomials of the second kind in several variables (see formula (4.3)), for the sum rulesJ s (i) introduced by K.M. Case [1] and studied by J.S. Dehesa et al. [2]–[3] in order to obtain informations about the zeros’ distribution of eigenfunctions of a class of ordinary polynomial differential operator, is derived.


Differential Operator Symmetric Function Representation Formula Polynomial Solution Negative Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Case K.M.,Sum rules for zeros of polynomials I–II, J. Math. Phys21 (1980), pp. 702–714.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Dehesa J.S., Buendia E., Sanchez Buendia M.A.,On the polynomial solution of ordinary differential equations of the fourth order, J. Math. Phys.26 (1985), pp. 1547–1552.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Buendia E., Dehesa J.S., Sanchez Buendia M.A.,On the zeros of eigenfunctions of polynomial differential operators, J. Math. Phys.26 (1985), pp. 2729–2736.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Raghavacharyulu I.V.V., Tekumalla A.R.,Solution of the Difference Equations of Generalized Lucas Polynomials, J. Math Phys. 13 (1972), pp. 321–324.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Bruschi M., Ricci P.E.,An explicit formula for f(A) and the generating function of the generalized Lucas polynomials, Siam J. Math. Anal.13 (1982), 162–165.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Bruschi M., Ricci P.E.,I polinomi di Lucas e di Tchebycheff in più variabili, Rend. Mat. (6)13 (1980), 507–530.MATHMathSciNetGoogle Scholar
  7. [7]
    Gradshteyn I.S., Ryzhik I.M.,Table of Integrals, Series, and Products, Academic Press, New York-London (1980).MATHGoogle Scholar

Copyright information

© Springer 1992

Authors and Affiliations

  • Paolo Emilio Ricci
    • 1
  1. 1.Dipartimento di MatematicaUniversità di Roma “La Sapienza”Roma

Personalised recommendations