Derivatives and Eulerian Numbers

Rza̧dkowski, Grzegorz

doi:10.1080/00029890.2008.11920551

Cited by 12 publications

(18 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The above formula (5) has been discussed during the Conference ICNAAM 2006 (September 2006) held in Greece and it appeared, with an inductive proof, in paper [6] (see also [7]). Independently, the formula has been considered and proved, with a proof based on generating functions, by Franssens [1].…”

Section: Logistic Equation and Logistic Functionmentioning

confidence: 99%

Logistic Function as a Tool of Planning

Rza̧dkowski

Głażewska

Sawińska

2014

Foundations of Management

View full text Add to dashboard Cite

In the present paper, we propose a new approach to investigate the logistic function, which is commonly used in mathematical models in economics and management. The approach is based on indicating in a given time series, having a logistic trend, some characteristic points corresponding to zeroes of successive derivatives of the logistic function. We also give examples of application of this method.

show abstract

Section: Logistic Equation and Logistic Functionmentioning

confidence: 99%

Logistic Function as a Tool of Planning

Rza̧dkowski

Głażewska

Sawińska

2014

Foundations of Management

View full text Add to dashboard Cite

show abstract

“….. The polynomials of the variable x on the right hand side of (17) are a particular case of the derivative polynomials which were introduced by Hoffman [12] and recently intensively studied (see for example [4], [5], [10], [18], [19]). Let us denote by Q n+1 (x) the derivative polynomial of the nth derivative of the function x(t) = 1/(1 + e t ) (where α = 0, β = 1), of degree n + 1.…”

Section: Derivative Polynomialsmentioning

confidence: 99%

“…We investigate expansions, which involve the falling factorials, for the Euler Gamma function and for the integral (18). The last is expressed in terms of the Riemann Zeta function.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 3 we present the basic properties of the derivative polynomials which are used in the next sections. Section 4 is devoted to the construction of the expansion for integral (18). For the coefficients of the expansion we give the recurrence formula and an explicit formula, which uses the coefficients of the Mittag-Leffler polynomials.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Rza̧dkowski

2012

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

In the present paper we introduce some expansions, based on the falling factorials, for the Euler Gamma function and the Riemann Zeta function. In the proofs we use the Faá di Bruno formula, Bell polynomials, potential polynomials, Mittag-Leffler polynomials, derivative polynomials and special numbers (Eulerian numbers and Stirling numbers of both kinds). We investigate the rate of convergence of the series and give some numerical examples.

show abstract

“…We will reformulate, to the case of complex holomorphic functions, some results of the paper [9]. Consider a holomorphic function z = z(t), defined in a domain t ∈ D ⊂ C which fulfils Riccati's differential equation with constant coefficients…”

Section: Two Theoremsmentioning

confidence: 99%