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11: 18.37 Classical OP’s in Two or More Variables
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Orthogonality
… ►The following three conditions, taken together, determine uniquely: … ►§18.37(ii) OP’s on the Triangle
… ►Orthogonality
… ►Orthogonal polynomials associated with root systems are certain systems of trigonometric polynomials in several variables, symmetric under a certain finite group (Weyl group), and orthogonal on a torus. …12: Bibliography N
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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Orthogonal polynomials.
Mem. Amer. Math. Soc. 18 (213), pp. v+185 pp..
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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Askey-Wilson polynomials: an affine Hecke algebra approach.
In Laredo Lectures on Orthogonal Polynomials and Special
Functions,
Adv. Theory Spec. Funct. Orthogonal Polynomials, pp. 111–144.
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13: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Some orthogonal
-polynomials.
Math. Nachr. 30, pp. 47–61.
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Characterization theorems for orthogonal polynomials.
In Orthogonal Polynomials (Columbus, OH, 1989),
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 294, pp. 1–24.
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Classical Orthogonal Polynomials.
In Orthogonal Polynomials and Applications, C. Brezinski, A. Draux, A. P. Magnus, P. Maroni, and A. Ronveaux (Eds.),
Lecture Notes in Math., Vol. 1171, pp. 36–62.
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14: Bibliography K
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Orthogonal Polynomials on -spheres: Gegenbauer, Jacobi and Heun.
In Topics in Polynomials of One and Several Variables and their
Applications,
pp. 299–322.
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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15: René F. Swarttouw
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►Swarttouw is mainly a teacher of mathematics and has published a few papers on special functions and orthogonal polynomials.
He is coauthor of the book Hypergeometric Orthogonal Polynomials and Their
-Analogues) Hypergeometric Orthogonal Polynomials and Their -Analogues.
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16: Bibliography G
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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
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Orthogonal Polynomials: Applications and Computation.
In Acta Numerica, 1996, A. Iserles (Ed.),
Acta Numerica, Vol. 5, pp. 45–119.
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Variable-precision recurrence coefficients for nonstandard orthogonal polynomials.
Numer. Algorithms 52 (3), pp. 409–418.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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17: Bibliography D
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Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach.
Courant Lecture Notes in Mathematics, Vol. 3, New York University Courant Institute of Mathematical
Sciences, New York.
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Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets.
SIAM J. Math. Anal. 30 (5), pp. 1029–1056.
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Inequalities for extreme zeros of some classical orthogonal and -orthogonal polynomials.
Math. Model. Nat. Phenom. 8 (1), pp. 48–59.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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18: 18 Orthogonal Polynomials
Chapter 18 Orthogonal Polynomials
…19: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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Orthogonal Polynomials in Coding Theory and Algebraic Combinatorics.
In Orthogonal Polynomials (Columbus, OH, 1989),
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 294, pp. 25–53.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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Padé-type Approximation and General Orthogonal Polynomials.
International Series of Numerical Mathematics, Vol. 50, Birkhäuser Verlag, Basel.
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