Iterated primitives of logarithmic powers (2009)
Medina, Luis A., Moll, Victor H., Rowland, Eric S.
The evaluation of iterated primitives of powers of logarithms is expressed in closed form. The expressions contain polynomials with coefficients given in terms of the harmonic numbers and their...
p-regularity of the p-adic valuation of the Fibonacci sequence (2009)
Medina, Luis A., Rowland, Eric S.
This paper studies the $p$-adic valuation of the sequence $\{F_n\}_{n \geq 1}$ of Fibonacci numbers from the perspective of regular sequences. We establish that this sequence is $p$-regular for every...
An Experimental Mathematics Perspective on the Old, and still Open, Question of When To Stop? (2009)
Medina, Luis A., Zeilberger, Doron
In a recent article in American Scientist, Theodore Hill described a coin-tossing game whose pay-off is the number of heads over the total number of throws. Suppose that at a given point during the...
The integrals in Gradshteyn and Ryzhik. Part 10: the digamma function (2007)
Medina, Luis A., Moll, Victor H.
Many integrals in the classical table by Gradshteyn and Ryzhik can be evaluated in terms of the digamma function (= the logarithmic derivative of the gamma function). Some of them are presented here.