Hermite%20polynomials
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8 matching pages
1: Bibliography I
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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On polynomials orthogonal with respect to certain Sobolev inner products.
J. Approx. Theory 65 (2), pp. 151–175.
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-Hermite polynomials, biorthogonal rational functions, and -beta integrals.
Trans. Amer. Math. Soc. 346 (1), pp. 63–116.
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Two families of orthogonal polynomials related to Jacobi polynomials.
Rocky Mountain J. Math. 21 (1), pp. 359–375.
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Classical and Quantum Orthogonal Polynomials in One Variable.
Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.
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2: 18.5 Explicit Representations
§18.5 Explicit Representations
… ►Hermite
… ►For corresponding formulas for Chebyshev, Legendre, and the Hermite polynomials apply (18.7.3)–(18.7.6), (18.7.9), and (18.7.11). … ►Hermite
… ►3: 28.8 Asymptotic Expansions for Large
4: Bibliography S
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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Uniform asymptotic expansions of Hermite polynomials.
M. Phil. thesis, City University of Hong Kong.
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On the relative extrema of the Hermite orthogonal functions.
J. Indian Math. Soc. (N.S.) 15, pp. 129–134.
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5: Bibliography K
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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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Zeros of exceptional Hermite polynomials.
J. Approx. Theory 200, pp. 28–39.
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6: 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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Algorithm 957: evaluation of the repeated integral of the coerror function by half-range Gauss-Hermite quadrature.
ACM Trans. Math. Softw. 42 (1), pp. 9:1–9:10.
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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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Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials.
J. Phys. A 47 (1), pp. 015203, 26 pp..
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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7: 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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Error bounds and exponential improvement for Hermite’s asymptotic expansion for the gamma function.
Appl. Anal. Discrete Math. 7 (1), pp. 161–179.
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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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8: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Connection between quantum systems involving the fourth Painlevé transcendent and -step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial.
J. Math. Phys. 57 (5), pp. Paper 052101, 15 pp..
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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Asymptotic expansions of ellipsoidal wave functions in terms of Hermite functions.
Math. Nachr. 32, pp. 49–62.
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