Temat: binomial - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Jordan numbers, Stirling numbers and sums of powers
Autorzy:: Wituła, Roman
Kaczmarek, Konrad
Lorenc, Piotr
Hetmaniok, Edyta
Pleszczyński, Mariusz
Powiązania:: https://bibliotekanauki.pl/articles/729201.pdf
Data publikacji:: 2014
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: Bernoulli numbers
binomial coefficients
Jordan numbers
Stirling numbers
Živković numbers
Opis:: In the paper a new combinatorical interpretation of the Jordan numbers is presented. Binomial type formulae connecting both kinds of numbers mentioned in the title are given. The decomposition of the product of polynomial of variable n into the sums of kth powers of consecutive integers from 1 to n is also studied.
Źródło:: Discussiones Mathematicae - General Algebra and Applications; 2014, 34, 2; 155-166
1509-9415
Pojawia się w:: Discussiones Mathematicae - General Algebra and Applications
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

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