Matrix methods in evaluation of integrals

• Autorzy: Wituła Roman , Słota Damian , Matlak Jarosław , Różański Michał

Identyfikatory

DOI

10.17512/jamcm.2020.1.09

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

matrix methods; evaluation of integrals; central binomial coefficients; identities for finite sums

PL

metoda macierzowa; współczynnik dwumianowy; metoda oceny całek

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2020
• Tom: Vol. 19, nr 1
• Strony: 103--112
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Wituła Roman

• Department of Mathematics, Silesian University of Technology, Gliwice, Poland

autor

Słota Damian

• Department of Mathematics Applications and Methods for Artificial Intelligence Silesian University of Technology, Gliwice, Poland

autor

Matlak Jarosław

• OpsTalent, Wrocław, Poland

autor

Różański Michał

• Department of Mathematics, Silesian University of Technology, Gliwice, Poland

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).