Volume 32 Issue 2 | Rocky Mountain Journal of Mathematics

Rocky Mountain Journal of Mathematics

VOL. 32 · NO. 2 | Summer 2002

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Front Matter

Table of Contents, Rocky Mountain Journal of Mathematics, vol. 32, no. 2, (2002)

Rocky Mountain J. Math. 32 (2), (Summer 2002) Open Access

No abstract available

Preface to Special Issue on Special Functions

Rocky Mountain J. Math. 32 (2), 389-390, (Summer 2002) Open Access

No abstract available

Articles

Parabolic Wavelet Transforms and Lebesgue Spaces of Parabolic Potentials

Ilham A. Aliev, Boris Rubin

Rocky Mountain J. Math. 32 (2), 391-408, (Summer 2002) DOI: 10.1216/rmjm/1030539677 Open Access

KEYWORDS: Wavelet transforms, parabolic potentials, Calderón's reproducing formula, anisotropic Lebesgue spaces, 42B99, 47G10, 46E35

No abstract available

A Multi-Index Borel-Dzrbashjan Transform

F. Al-Musallam, V. Kiryakova, V. Kim Tuan

Rocky Mountain J. Math. 32 (2), 409-429, (Summer 2002) DOI: 10.1216/rmjm/1030539678 Open Access

KEYWORDS: Laplace-type integral transform, Mittag-Leffler function, $h$-transform, operators of fractional integration and differentiation, BorelDzrbashian transform, 44A15, 44A30, 26A33, 33E12, 33C60

No abstract available

Some $q$-Orthogonal Polynomials and Related Hankel Determinants

G. Andrews, J. Wimp

Rocky Mountain J. Math. 32 (2), 429-442, (Summer 2002) DOI: 10.1216/rmjm/1030539679 Open Access

No abstract available

On Sampling Associated with Singular Sturm-Liouvile Eigenvalue Problems: The Limit-Cycle Case

M.H. Annaby, P.L. Butzer

Rocky Mountain J. Math. 32 (2), 443-466, (Summer 2002) DOI: 10.1216/rmjm/1030539680 Open Access

KEYWORDS: sampling theory, singular Sturm-Liouville problems, Legendre functions of first and second kind, Bessel's functions, 41A05, 34B05, 94A20

No abstract available

Orthogonal Polynomials with Respect to a Differential Operator. Existence and Uniqueness

A.I. Aptekarev, G.T.L. Lagomasino, F. Marcellán

Rocky Mountain J. Math. 32 (2), 467-481, (Summer 2002) DOI: 10.1216/rmjm/1030539681 Open Access

KEYWORDS: Tchebyshev systems, Sobolev orthogonality differential operators, 42C05

No abstract available

Algebra of Differential Forms with Exterior Differential $d^3=0$ in Dimensions One and Two

N. Bazunova

Rocky Mountain J. Math. 32 (2), 483-497, (Summer 2002) DOI: 10.1216/rmjm/1030539682 Open Access

No abstract available

From Non-Hermitian Oscillator-Like Operators to Freud Polynomials and Some Consequences

N. Debergh

Rocky Mountain J. Math. 32 (2), 499-506, (Summer 2002) DOI: 10.1216/rmjm/1030539683 Open Access

No abstract available

Pick Functions Related to the Gamma Function

Christian Berg, Henrik L. Pedersen

Rocky Mountain J. Math. 32 (2), 507-525, (Summer 2002) DOI: 10.1216/rmjm/1030539684 Open Access

KEYWORDS: Gamma function, completely monotone function, 33B15, 30E20, 30E15

No abstract available

Linear Rational Interpolation and Its Application in Approximation and Boundary Value Problems

Jean-Paul Berrut, Hans D. Mittelmann

Rocky Mountain J. Math. 32 (2), 527-545, (Summer 2002) DOI: 10.1216/rmjm/1030539685 Open Access

KEYWORDS: Linear rational interpolation, linear rational collocation, pole optimization, 65D05, 65L10, 41A05, 41A20

No abstract available

Dirichlet Splines as Fractional Integrals of $B$-Splines

Wolfgang Zu Castell

Rocky Mountain J. Math. 32 (2), 545-559, (Summer 2002) DOI: 10.1216/rmjm/1030539686 Open Access

KEYWORDS: Dirichlet averages, Dirichlet splines, divided differences, $B$-splines, Dirichlet distribution, fractional integrals and derivatives, 41A15, 62H10, 26A33

No abstract available

Inversion Techniques and Combinatorial Identities: Balanced Hypergeometric Series

Chu Wenchang

Rocky Mountain J. Math. 32 (2), 561-588, (Summer 2002) DOI: 10.1216/rmjm/1030539687 Open Access

KEYWORDS: hypergeometric series, duplicate inverse series relations, 33C20, 05A19

No abstract available

A Non-Automatic (!) Application of Gosper's Algorithm Evaluates a Determinant from Tiling Enumeration

M. Ciucu, C. Krattenthaler

Rocky Mountain J. Math. 32 (2), 589-607, (Summer 2002) DOI: 10.1216/rmjm/1030539688 Open Access

KEYWORDS: 05A15, 05A16, 05A17, 05A19, 05B45, 33C20, 52C20

No abstract available

Partial Differential Equations Satisfied by Polynomials which Have a Product Formula

William C. Connett, Alan L. Schwartz

Rocky Mountain J. Math. 32 (2), 607-636, (Summer 2002) DOI: 10.1216/rmjm/1030539689 Open Access

KEYWORDS: 35P99, 47L80, 33C50, 43A62, 43A10

No abstract available

Elliptic Beta Integrals and Mudular Hypergeometric Sums: An Overview

J.F. van Diejen, V.P. Spiridonov

Rocky Mountain J. Math. 32 (2), 639-656, (Summer 2002) DOI: 10.1216/rmjm/1030539690 Open Access

No abstract available

An Inverse to the Askey-Wilson Operator

Mourad E.H. Ismail, Mizan Rahman

Rocky Mountain J. Math. 32 (2), 657-678, (Summer 2002) DOI: 10.1216/rmjm/1030539691 Open Access

KEYWORDS: weight functions, inverse operator, Integral‎ ‎Operators, divided difference operators, continuous $q$-Jacobi polynomials, monotonicity of kernels, $t$-commutators, 33D15, 47B34

No abstract available

A Fourth Order $q$-Difference Equation for Associated Discrete $q$-Orthogonal Polynomials

Mourad E.H. Ismail, Plamen Simeonov

Rocky Mountain J. Math. 32 (2), 679-690, (Summer 2002) DOI: 10.1216/rmjm/1030539692 Open Access

No abstract available

Generalized Umemura Polynomials

Anatol N. Kirillov, Makoto Taneda

Rocky Mountain J. Math. 32 (2), 691-703, (Summer 2002) DOI: 10.1216/rmjm/1030539693 Open Access

No abstract available

Transmutation Kernels for the Little $q$-Jacobi Function Theorem

Erik Koelink, Hjalmar Rosengren

Rocky Mountain J. Math. 32 (2), 703-738, (Summer 2002) DOI: 10.1216/rmjm/1030539694 Open Access

KEYWORDS: Summation formula, transmutation kernels, product formula, little $q$-Jacobi function, intertwiner, fractional $q$-integral operator, 33D15, ‎33D45, 47B36

No abstract available

Division Problem of Moment Functionals

J.H. Lee, K.H. Kwon

Rocky Mountain J. Math. 32 (2), 739-758, (Summer 2002) DOI: 10.1216/rmjm/1030539695 Open Access

KEYWORDS: Quasi-definiteness, moment functionals, Division problem, 33C45

No abstract available

A New $A_n$ Extension of Ramanujan's ${}_1\psi_1$ Summation with Applications to Multilateral An Series

Stephen C. Milne, Michael Schlosser

Rocky Mountain J. Math. 32 (2), 759-793, (Summer 2002) DOI: 10.1216/rmjm/1030539696 Open Access

KEYWORDS: Bilateral basic hypergeometric series, $q$-series, multiple basic hypergeometric series associated to the root system An, $U_( n + 1)$ series, $q$-binomial theorem, Ramanujan's ${}_1\psi_1$ summation, Macdonald identities, Bailey's ${}_2\psi_2$ transformations, ${}_2\psi_2$ summation, 33D15, 05A19, 33D67

No abstract available

Multiple Gamma Function, Its $q$- and Elliptic Analogue

Michitomo Nishizawa

Rocky Mountain J. Math. 32 (2), 793-811, (Summer 2002) DOI: 10.1216/rmjm/1030539697 Open Access

No abstract available

Numerical Calculations of the Generalized Sine and Cosine Integral

K.-D. Reinsch, R. Bulirsch, U. Puschmann

Rocky Mountain J. Math. 32 (2), 813-826, (Summer 2002) DOI: 10.1216/rmjm/1030539698 Open Access

No abstract available

Leonard Pairs from 24 Points of View

Paul Terwilliger

Rocky Mountain J. Math. 32 (2), 827-888, (Summer 2002) DOI: 10.1216/rmjm/1030539699 Open Access

KEYWORDS: $q$-Racah polynomial, Leonard pair, tridiagonal pair, Askey scheme, Askey-Wilson polynomials, 05E30, 05E35, 33C45, ‎33D45

No abstract available

Inversion of the Dunkl Intertwining Operator and Its Dual Using Dunkl Wavelets

Khalifa TriÈmche

Rocky Mountain J. Math. 32 (2), 889-917, (Summer 2002) DOI: 10.1216/rmjm/1030539700 Open Access

No abstract available

A Generalization of Kummer's Identity

Raimundas Vidunas

Rocky Mountain J. Math. 32 (2), 919-936, (Summer 2002) DOI: 10.1216/rmjm/1030539701 Open Access

KEYWORDS: 33C05, 33F10, 39A10

No abstract available

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