Evaluation of the Fermi-Dirac integral of half-integer order
Eventual positivity for analytic functions.
Excursions of diffusion processes and continued fractions
It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process. We show that, in many cases of interest, the Riccati equation can be solved in terms of an infinite continued fraction. We examine the probabilistic significance of the expansion. To illustrate our results, we discuss some examples of diffusions in deterministic and in random environments.
Exemples de fonctions à espaces lacunaires
Existence des valeurs limites du produit d'Hadamard
Expansion of analytic functions in series of classical orthogonal polynomials
Extending analyticK-subanalytic functions
Letg:U→ℝ (U open in ℝn) be an analytic and K-subanalytic (i. e. definable in ℝanK, whereK, the field of exponents, is any subfield ofℝ) function. Then the set of points, denoted Σ, whereg does not admit an analytic extension is K-subanalytic andg can be extended analytically to a neighbourhood of Ū.
Extension of analytic number theory and the theory of regularized harmonic series from Dirichlet series to Bessel series.
Extremely non-normal continued fractions