90.39 On a family of polynomials

93.12 Some integral representations for Bernoulli numbers

“…with integer coefficients, where n = 0,1,2, ... . In [2] two formulae for these polynomials are proved. The first is the recurrence formula fp"(t)dt = -ft (9) forn = 1,2,3... .…”

“…The first few non-zero Bernoulli numbers are Bo = 1, B\ ~ -, Bo = -, BA = ,5fi = -, Bs = , It is proved in[2] that the n th derivative of the function (1) is…”

Logistic Function as a Tool of Planning

“…The polynomial, of order 5is known in the literature as the derivative polynomial. It can be proved (see [8]) that all…”

On some expansions for the Euler Gamma function and the Riemann Zeta function

“…Independently the formula has been considered and proved, with a proof based on generating functions, by Franssens [10] (see also [17]). If a function x(t) satisfies equation (16), then the nth derivative of x(t) can be expressed by the following formula:…”

“…In the paper [17] (see also [4], [5], [10]) it is proved that the polynomials Q n (x) can be expressed in terms of the Stirling numbers of the second kind n k (number of the ways of partitioning a set of n elements into k nonempty subsets, see Graham et al [11]), namely…”