Stimulated by earlier work by Moll and his coworkers [1], we evaluate various basic log Gamma integrals in terms of partial derivatives of Tornheim– Witten zeta functions and their extensions arising from evaluations of Fourier series. In particular, we fully evaluate

We study the properties of a logconcavity operator on a symmetric, unimodal subset of finite sequences. In doing so we are able to prove that there is a large unbounded region in this subset that is ∞-logconcave. This problem was motivated by the conjecture of Moll and Boros in [1] that the binomial coefficients are ∞-logconcave.

Let a, b and n be positive integers with a > b. In this note, we prove that (2bn + 1)(2bn + 3) ( 2bn bn )∣∣∣∣3(a− b)(3a− b)(2an an )( an bn ) . This confirms a recent conjecture of Amdeberhan and Moll.

The Boros-Moll polynomials arise in the evaluation of a quartic integral. The original double summation formula does not imply the fact that the coefficients of these polynomials are positive. Boros and Moll proved the positivity by using Ramanujan’s Master Theorem to reduce the double sum to a single sum. Based on the structure of reluctant functions introduced by Mullin and Rota along with an...

This Commentary is a response to Moll (S Afr J Sci. 2023;119(1/2), Art. #12916) who refutes the Fourth Industrial Revolution (4IR) and its impact. As this demonstrates, there case be made that 4IR constitutes revolution limitation at level of pure technology can refuted as based on wider While classified an evolution Third Revolution, scale, scope complexity denote own.

The ratio monotonicity of a polynomial is a stronger property than log-concavity. Let P (x) be a polynomial with nonnegative and nondecreasing coefficients. We prove the ratio monotone property of P (x+ 1), which leads to the log-concavity of P (x+ c) for any c ≥ 1 due to Llamas and Mart́ınez-Bernal. As a consequence, we obtain the ratio monotonicity of the Boros-Moll polynomials obtained by Che...