Estimating the sequence of real binomial coefficients.
Estimation in models driven by fractional brownian motion
Let {bH(t), t∈ℝ} be the fractional brownian motion with parameter 0<H<1. When 1/2<H, we consider diffusion equations of the type X(t)=c+∫0tσ(X(u)) dbH(u)+∫0tμ(X(u)) du. In different particular models where σ(x)=σ or σ(x)=σ x and μ(x)=μ or μ(x)=μ x, we propose a central limit theorem for estimators of H and of σ based on regression methods. Then we give tests of the hypothesis on σ for these models. We also consider functional estimation on σ(⋅)...
Estimations at infinity of Bessel functions associated to the representations of a Jordan algebra. (Estimations à l'infini des fonctions de Bessel associées aux représentations d'une algèbre de Jordan.)
Étude des fonctions de Fourier (première et deuxième espèce)
Euler polynomials and the related quadrature rule.
Eulerian numbers with fractional order parameters.
Evaluation of associated Legendre functions off the cut and parabolic cylinder functions.
Evaluation of the Fermi-Dirac integral of half-integer order
Evaluation of the half-periods of the Weierstrass -function for the absolute invariant greater than one
Evaluation of triple Euler sums.
Evaluations of some determinants of matrices related to the Pascal triangle.
Evaluations of the Rogers-Ramanujan continued fraction R(q) by modular equations
Exact and approximate distributions for the product of Dirichlet components
It is well known that has the beta distribution when and follow the Dirichlet distribution. Linear combinations of the form have also been studied in Provost and Cheong [S. B. Provost and Y.-H. Cheong: On the distribution of linear combinations of the components of a Dirichlet random vector. Canad. J. Statist. 28 (2000)]. In this paper, we derive the exact distribution of the product (involving the Gauss hypergeometric function) and the corresponding moment properties. We also propose...
Exact solution of convective mass transfer model for calcium response of endothelium.
Exact solutions of the semi-infinite Toda lattice with applications to the inverse spectral problem.
Exotic approximate identities and Maass forms
We obtain some approximate identities whose accuracy depends on the bottom of the discrete spectrum of the Laplace-Beltrami operator in the automorphic setting and on the symmetries of the corresponding Maass wave forms. From the geometric point of view, the underlying Riemann surfaces are classical modular curves and Shimura curves.
Exotic Bailey-Slater spt-functions III: Bailey pairs from groups B, F, G, and J
We continue to investigate spt-type functions that arise from Bailey pairs. In this third paper on the subject, we proceed to introduce additional spt-type functions. We prove simple Ramanujan type congruences for these functions which can be explained by an spt-crank-type function. The spt-crank-type functions are actually defined first, with the spt-type functions coming from setting z = 1 in this definition. We find some of the spt-crank-type functions to have interesting representations as single...
Expansion formulae for Bessel functions in series of Bessel functions
Expansion formulae for the products of Meijer's G-function and Bessel functions
Expansion of a class of functions into an integral involving associated Legendre functions.