On some Turán-type inequalities

We prove Turan-type inequalities for some special functions by using a generalization of the Schwarz inequality

Remarks on Bell and higher order Bell polynomials and numbers

We recover a recurrence relation for representing in an easy form the coefficients $A_{n,k}$ of the Bell polynomials, which are known in literature as the partial Bell polynomials. Several applications in the framework of classical calculus are derived, avoiding the use of operational techniques. Furthermore, we generalize this result to the coefficients $A^{[2]}_{n,k}$ of the second-order Bell polynomials, i.e. of the Bell polynomials relevant to nth derivative of a composite function of the type f(g(h(t))). The second-order Bell polynomials $B_n^{[2]}$ and the relevant Bell numbers $b_n^{[2]}$ are introduced. Further extension of the nth derivative of M-nested functions is also touched on

Adjoint Appell-Euler and First Kind Appell-Bernoulli Polynomials

The adjunction property, recently introduced for Sheffer polynomial sets, is considered in the case of Appell polynomials. The particular case of adjoint Appell-Euler and Appell-Bernoulli polynomials of the first kind is analyzed

ZEROS OF BESSEL FUNCTIONS: MONOTONICITY, CONCAVITY, INEQUALITIES

We present a survey of the most important inequalities and monotonicity, concavity (convexity) results of the zeros of Bessel functions. The results refer to the definition Jνκ of the zeros of Cν (x) = Jν (x) cosα −Yν (x) sinα, formulated in [6], where κ is a continuous variable. Sometimes, also the Sturm comparison theorem is an important tool of our results.We present a survey of the most important inequalities and monotoni-city, concavity (convexity) results of the zeros of Bessel functions. Theresults refer to the definition Jνκ of the zeros of Cν (x) = Jν (x) cosα −Yν (x) sinα, formulated in [6], where κ is a continuous variable. Sometimes, also the Sturm comparison theorem is an important tool of our results