Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: tożsamość trygonometryczna

Sortuj według:

Ogranicz wyniki do:

Symbolic description of the polynomial roots and their numerical implementation - better than in Mathematica software?

Hetmaniok Edyta, Słota Damian, Pleszczyński Mariusz, Wituła Roman, Różański Michał, Szczygieł Marcin

Annals of Computer Science and Information Systems

2019

Vol. 20

41--45

This paper is a continuation of the discussion undertaken in one of our previous papers. We present in the current paper the corrected, and also given in a slightly changed form, Vandermonde formulae for the roots of some quintic polynomials considered in J.P. Tignol's monograph. The proofs of selected trigonometric identities from our previous paper are given and some new identities have been generated by the occasion, which also can be used for testing our Langrange algorithm for the case of cubic polynomials. Moreover, we present here the decomposition of polynomials belonging to some two-parameter family of polynomials related to the Chebyshev polynomials of the first kind.

Remarkable identities

Górowski J., Żabowski J.

Journal of Mathematics and Applications

2014

Vol. 37

39--50

In the paper a number of identities involving even powers of the values of functions tangent, cotangent, secans and cosecans are proved. Namely, the following relations are shown: [wzory] where m, n are positive integers, f is one of the functions: tangent, cotangent, secans or cosecans and wf(x),vf(x),~wf(x) are some polynomials from Q[x]. One of the remarkable identities is the following: [wzór] Some of these identities are used to find, by elementary means, the sums of the series of the form [wzór] , where n is a fixed positive integer. One can also notice that Bernoulli numbers appear in the leading coeficients of the polynomials wf(x),vf(x) and ~ wf(x).