A combined symbolic and numerical algorithm for the computation of zeros of orthogonal polynomials and special functions

DOI10.1016/S0747-7171(03)00013-0zbMath1024.65039OpenAlexW2079823288MaRDI QIDQ1404414

Javier Segura, Amparo Gil

Publication date: 21 August 2003

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0747-7171(03)00013-0

zbMATH Keywords

performanceorthogonal polynomialsnumerical examplessymbolic computationspecial functionsHermite polynomialLegendre polynomialpolynomial zerosBessel functionGegenbauer polynomialChebyshev polynomialthree-term recurrence relationJacobi polynomialfixed point iterationsMaple algorithmconical functionsCoulomb function

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Computation of special functions and constants, construction of tables (65D20) Numerical computation of solutions to single equations (65H05) Numerical approximation and evaluation of special functions (33F05) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (3)

On the zeros and turning points of special functions. ⋮ Asymptotic-numerical approximations for highly oscillatory second-order differential equations by the phase function method ⋮ On the properties of zeros of Bessel series in the real line

Uses Software

• Maple
• RFSFNS
• ELF
• GNOME
• ALGOL 60

Cites Work

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• An algorithm with ALGOL 60 program for the computation of the zeros of ordinary Bessel functions and those of their derivatives
• Computing zeros and orders of Bessel functions
• RFSFNS: A portable package for the numerical determination of the number and the calculation of roots of Bessel functions
• A global Newton method for the zeros of cylinder functions
• ELF and GNOME: two tiny codes to evaluate the real zeros of the Bessel functions of the first kind for real orders
• On the zeros and turning points of special functions.
• Computing the real zeros of hypergeometric functions
• On the structure of recurrence relations. II
• Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros
• On the Monotonicity of Certain Riesz Means
• The Zeros of Regular Coulomb Wave Functions and of Their Derivative
• The Zeros of Special Functions from a Fixed Point Method
• Calculation of Gauss Quadrature Rules

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