Let JÎ¼ denote the Bessel function of order Î¼. The functions xJÎ±+Î²+2n+1(x 1/2), n = 0, 1, 2, . . . , form an orthogonal system in L2((0,âˆž), xÎ±+Î²dx) when Î±+ Î² > âˆ’1. In this paper we analyze the rangeâ€¦ (More)

Computer algebra systems are a great help for mathematical research but sometimes unexpected errors in the software can also badly affect it. As an example, we show how we have detected an error ofâ€¦ (More)

Hurwitz found the Fourier expansion of the Bernoulli polynomials over a century ago. In general, Fourier analysis can be fruitfully employed to obtain properties of the Bernoulli polynomials andâ€¦ (More)

We prove two-weight norm inequalities for CesÃ ro means of generalized Hermite polynomial series and for the supremum of these means. A result about weak boundedness and an almost everywhereâ€¦ (More)

The study of the convergence of Snf in L(dÎ±) (p 6= 2) has been discussed for several classes of orthogonal polynomials (c.f. Askey-Wainger [1], Badkov [2â€“ 4], Muckenhoupt [11â€“13], Newman-Rudin [16],â€¦ (More)

We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type (1, 1) inequalities. As anâ€¦ (More)

For complex parameters Î» and s, consider the Lerch transcendent Î¦(Î», s, z) = âˆ‘âˆž k=0 Î» (k + z)âˆ’s as a function of the complex variable z. We analyze the asymptotic behavior of this function as Re sâ†’â€¦ (More)

In this paper we describe some advances in the knowledge of the behavior of aliquot sequences starting with a number less than 10000. For some starting values, it is shown for the first time that theâ€¦ (More)