Autor: Słota, Damian - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Families of Increasing Sequences Possessing the Harmonic Series Property
Autorzy:: Wituła, Roman
Hetmaniok, Edyta
Słota, Damian
Powiązania:: https://bibliotekanauki.pl/articles/972271.pdf
Data publikacji:: 2013
Wydawca:: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:: Sierpiński family
harmonic series property
Opis:: We prove in this paper that any maximal, with respect to inclusion, subset of N – the family of all increasing sequences of positive integers – possessing the harmonic series property has the cardinality of the continuum. Moreover, we prove that for any countable (infinite) set exists an "orthogonal" family such that it hold some facts. All facts are proved constructively, by using the modified version of the classical Sierpiński family of increasing sequences having the cardinality of the continuum.
Źródło:: Acta Universitatis Lodziensis. Folia Mathematica; 2013, 18
2450-7652
Pojawia się w:: Acta Universitatis Lodziensis. Folia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Matrix methods in evaluation of integrals
Autorzy:: Wituła, Roman
Słota, Damian
Matlak, Jarosław
Różański, Michał
Powiązania:: https://bibliotekanauki.pl/articles/122939.pdf
Data publikacji:: 2020
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: matrix methods
evaluation of integrals
central binomial coefficients
identities for finite sums
metoda macierzowa
współczynnik dwumianowy
metoda oceny całek
Opis:: The method of evaluating the integrals through use of the matrix inversion, presented here, was introduced by J.W. Rogers and then generalized by Matlak, Słota and Wituła. This method is still developed and one of its other possible applications is presented in this paper. This application concerns a new way of evaluating the integral ʃ sec²ⁿ⁺¹ xdx on the basis of the discussed method. Additionally, many other applications of the obtained original recursive formula for this type of integral are given here. Some of them are used to generate the interesting identities for inverses of the central binomial coefficients and the trigonometric limits. The historical view is also presented as well as the connections between the received and previously known identities.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 103-112
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Matrix methods in evaluation of integrals
Autorzy:: Wituła, Roman
Słota, Damian
Matlak, Jarosław
Różański, Michał
Powiązania:: https://bibliotekanauki.pl/articles/1839805.pdf
Data publikacji:: 2020
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: matrix methods
evaluation of integrals
central binomial coefficients
identities for finite sums
metoda macierzowa
współczynnik dwumianowy
metoda oceny całek
Opis:: The method of evaluating the integrals through use of the matrix inversion, presented here, was introduced by J.W. Rogers and then generalized by Matlak, Słota and Wituła. This method is still developed and one of its other possible applications is presented in this paper. This application concerns a new way of evaluating the integral ʃ sec2n+1 xdx on the basis of the discussed method. Additionally, many other applications of the obtained original recursive formula for this type of integral are given here. Some of them are used to generate the interesting identities for inverses of the central binomial coefficients and the trigonometric limits. The historical view is also presented as well as the connections between the received and previously known identities.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 103-112
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

Artykuł

Informacja