Differentiation and integration by using matrix inversion

Matlak, Dagmara; Matlak, Jarosław; Słota, Damian; Wituła, Roman

doi:10.17512/jamcm.2014.2.07

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“…We note that the method of evaluating I n , presented in the current paper, is different than the previously discussed methods of analytical-combinatoric nature [1,6,7]. The method of evaluating the integrals, presented here, was introduced by Rogers in paper [8] and generalized by Matlak, Słota and Wituła in [9]. The method was also discussed by Meemark and Sriwongsa in the paper [10].…”

Section: Introductionmentioning

confidence: 92%

Matrix methods in evaluation of integrals

Wituła¹,

Słota²,

Matlak³

et al. 2020

J. Appl. Math. Comput. Mech.

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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 sec 2n+1 x dx 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.

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