Extensions of inequalities of the Laguerre and Turan type

DOI10.2140/pjm.1973.44.675zbMath0265.33012OpenAlexW2014938221MaRDI QIDQ2562277

Merrell L. Patrick

Publication date: 1973

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.1973.44.675

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Spherical harmonics (33C55) Representations of entire functions of one complex variable by series and integrals (30D10)

Related Items (23)

Bounds for zeros of the Laguerre polynomials ⋮ Turán determinants of Bessel functions ⋮ When does a hypergeometric function \(_pF_q\) belong to the Laguerre-Pólya class \(LP^+\)? ⋮ The generalized Laguerre inequalities and functions in the Laguerre-Pólya class ⋮ Laguerre inequalities for discrete sequences ⋮ Fourier transforms of positive definite kernels and the Riemann \(\xi\)-function ⋮ Properties arising from Laguerre-Pólya class for the Boros-Moll numbers ⋮ Necessary and sufficient conditions and the Riemann hypothesis ⋮ Jensen polynomials with applications to the Riemann \(\xi\)-function ⋮ The Laguerre inequalities with applications to a problem associated with the Riemann hypothesis ⋮ Log-concavity and Turán-type inequalities for the generalized hypergeometric function ⋮ On the behavior of Gegenbauer polynomials in the complex plane ⋮ Approximations for the Bessel and Airy functions with an explicit error term ⋮ Stable regions of Turán expressions ⋮ Stability of the Landau-Fermi liquid theory ⋮ Turán inequalities for three-term recurrences with monotonic coefficients ⋮ Elements of Pólya-Schur theory in the finite difference setting ⋮ DISCRETE ANALOGUES OF THE LAGUERRE INEQUALITY ⋮ A new class of non-linear stability preserving operators ⋮ On some questions of Fisk and Brändén ⋮ Turán type inequalities for regular Coulomb wave functions ⋮ Proof of a conjecture of M. Patrick concerning Jacobi polynomials ⋮ Inequalities for real-root polynomials and entire functions

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