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 monotonicity property of the -function.
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...
A multiplier theorem for Jacobi expansions
A multiplier theorem for ultraspherical series
A naive-topological study of the contiguity relations for hypergeometric functions
When the parameters are real, the hypergeometric equation defines a Schwarz triangle. We study a combinatorial-topological property of the Schwarz triangle when the three angles are not necessarily less than π.
A new approach to the Dyson coefficients.
A new approach to the problem of constructing recurrence relations for the Jacobi coefficients
A new characteristic property of Mittag-Leffler functions and fractional cosine functions
A new characteristic property of the Mittag-Leffler function with 1 < α < 2 is deduced. Motivated by this property, a new notion, named α-order cosine function, is developed. It is proved that an α-order cosine function is associated with a solution operator of an α-order abstract Cauchy problem. Consequently, an α-order abstract Cauchy problem is well-posed if and only if its coefficient operator generates a unique α-order cosine function.
A new characterization of Euler's gamma function by a functional equation.
A new characterization of Euler's gamma function by a functional equation.
A new class of Bessel function integrals.
A new criterion for close-to-convexity of partial sums of certain hypergeometric functions.
A new family of functional series relations involving digamma functions
A new form of the spherical expansion of zonal functions and Fourier transforms of -finite functions.
A new functional equation characterizing generalized Joukowski transformations.
A new generalized theorem on Fox's H-function.
A new generating function of (-) Bernstein-type polynomials and their interpolation function.
A new irrationality measure for ζ(3)