Luigi Gatteschi's work on asymptotics of special functions and their zeros

DOI10.1007/s11075-008-9208-5zbMath1170.26007OpenAlexW1985305079MaRDI QIDQ1014768

Carla Giordano, Walter Gautschi

Publication date: 29 April 2009

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-008-9208-5

zbMATH Keywords

asymptoticszerosspecial functionsLuigi Gatteschi's work

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Real polynomials: location of zeros (26C10) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items (6)

Application of the Liouville-Steklov method to estimation of error of a Hilb type formula for Jacobi polynomials ⋮ Studies on the zeros of Bessel functions and methods for their computation. II: Monotonicity, convexity, concavity, and other properties ⋮ New conjectured inequalities for zeros of Jacobi polynomials ⋮ On a conjectured inequality for the largest zero of Jacobi polynomials ⋮ Biographic notes on Luigi Gatteschi ⋮ Experimental Mathematics Involving Orthogonal Polynomials

Uses Software

• BIJ

Cites Work

• Sul comportamento asintotico delle funzioni di Bessel di prima specie di ordine ed argomento quasi uguali
• How sharp is Bernstein's inequality for Jacobi polynomials?
• On a conjectured inequality for the largest zero of Jacobi polynomials
• Una nuova rappresentazione asintotica dei polinomi ultrasferici
• Remarks on asymptotics for Jacobi polynomials
• Asymptotics and bounds for the zeros of Laguerre polynomials: A survey
• On a method for generating inequalities for the zeros of certain functions
• Sugli zeri delle funzioni di cui si conosce una rappresentazione asintotica
• Valutazione dell'errore nella formula di McMahon per gli zeri della funzione \(J_0 (kz) Y_0 (z) - J_0 (z) Y_0 (kz)\)
• Expansion of the hypergeometric function in series of confluent ones and application to the Jacobi polynomials
• Il termine complementare nella formula di Hilb-Szegö ed una nuova valutazione asintotica degli zeri dei polinomi ultrasferici
• Sulla rappressentazione asintotica delle funzioni di Bessel di uguale ordine ed argomento
• A Uniform Asymptotic Expansion of the Jacobi Polynomials with Error Bounds
• New Inequalities for the Zeros of Jacobi Polynomials
• Uniform Asymptotic Expansions of Laguerre Polynomials
• Uniform Asymptotic Expansions for Whittaker’s Confluent Hypergeometric Functions
• A Bernstein-Type Inequality for the Jacobi Polynomial
• Error bounds for mcmahon's asympotic approximations of the zeros of the bessel functions
• Uniform Asymptotic Expansions of the Jacobi Polynomials and an Associated Function
• New asymptotics for the zeros of Whittaker's functions
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