Some generalizations of Gregory's power series and their applications

• Autorzy: Gawrońska N. , Słota D. , Wituła R. , Zielonka A.
• Języki publikacji: EN

Abstrakty

EN

The series representing the generalizations of classical James Gregory's series are discussed in this paper. Formulae describing sums of these series are found. A number of applications of obtained formulae are also presented, among others, in receiving the generalizations of Gregory-Leibniz-Nilakantha formula. Moreover, the sums of series of differences of odd harmonic numbers are generated.

Słowa kluczowe

EN

Gregory’s series; Gregory-Leibniz-Nilakantha formula

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2013
• Tom: Vol. 12, nr 3
• Strony: 79--91
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Gawrońska N.

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

autor

Słota D.

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

autor

Wituła R.

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

autor

Zielonka A.

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

Bibliografia

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• [3] Wituła R., Słota D., On the sum of some alternating series, Comput. Math. Appl. 2011, 62, 2658-2664.
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• [5] Wituła R., Complex Numbers, Polynomials and Partial Fractions Decompositions, Part I, Wyd. Pol. Śl., Gliwice 2010 (in Polish).
• [6] Knopp K., Infinite Series, PWN, Warsaw 1956 (in Polish).
• [7] Wituła R., On certain applications of formulae for sum of unimodular complex numbers, Wyd. Prac. Komputerowej J. Skalmierskiego, Gliwice 2011 (in Polish).
• [8] Edwards C.H., The Historical Development of the Calculus, Springer, New York 1979.
• [9] Prudnikov A.P., Brychkov Yu.A., Marichev O.I., Integrals and Series, Vol. 1, Elementary Functions, Gordon & Breach Sci. Pub., New York 1986.
• [10] Bromwich T.J.I'A., An Introduction to the Theory of Infinite Series, Merchant Books 2008.
• [11] Prus-Wiśniowski F., Real Series, Wyd. Nauk. Uniw. Szczecińskiego, Szczecin 2005 (in Polish).