A curious integral.
A deformation of commutative polynomial algebras in even numbers of variables
We introduce and study a deformation of commutative polynomial algebras in even numbers of variables. We also discuss some connections and applications of this deformation to the generalized Laguerre orthogonal polynomials and the interchanges of right and left total symbols of differential operators of polynomial algebras. Furthermore, a more conceptual re-formulation for the image conjecture [18] is also given in terms of the deformed algebras. Consequently, the well-known Jacobian conjecture...
A determinant identity that implies Rogers-Ramanujan.
A family of tridiagonal pairs related to the quantum affine algebra .
A fast algorithm for the construction of recurrence relations for modified moments
A new approach is presented for constructing recurrence relations for the modified moments of a function with respect to the Gegenbauer polynomials.
A Fast Transform for Spherical Harmonics.
A finite integral involving a confluent hypergeometric function and Meijer's G-function
A general quadrature formula using zeros of spherical Bessel functions as nodes
We obtain, for entire functions of exponential type satisfying certain integrability conditions, a quadrature formula using the zeros of spherical Bessel functions as nodes. We deduce from this quadrature formula a result of Olivier and Rahman, which refines itself a formula of Boas.
A generalization of Bateman's expansion and finite integrals of Sonine's and Feldheim's type
Let be a sequence of arbitrary complex numbers, let α,β > -1, let Pₙα,βn=0+∞
A generalization of the Bernoulli polynomials.
A generalization of the Weber-Schafheitlin integral.
A generalized beta function and associated probability density.
A generalized inversion formula for the continuous Jacobi transform.
A geometric study of the hypergeometric function with imaginary exponents.
A geometrical proof of a new inequality for the gamma function.
A limit relation for Dunkl-Bessel functions of type A and B.
A Markov Type Inequality for Higher Derivates of Polynomials.
A matrix analysis of the stability of the Clenshaw algorithm.
A model for proportions with medical applications
Data that are proportions arise most frequently in biomedical research. In this paper, the exact distributions of R = X + Y and W = X/(X+Y) and the corresponding moment properties are derived when X and Y are proportions and arise from the most flexible bivariate beta distribution known to date. The associated estimation procedures are developed. Finally, two medical data sets are used to illustrate possible applications.
A multimodal beta distribution with application to economic data
Beta distributions are popular models for economic data. In this paper, a new multimodal beta distribution with bathtub shaped failure rate function is introduced. Various structural properties of this distribution are derived, including its cdf, moments, mean deviation about the mean, mean deviation about the median, entropy, asymptotic distribution of the extreme order statistics, maximum likelihood estimates and the Fisher information matrix. Finally, an application to consumer price indices...