Vsote potenc : delo diplomskega seminarja

Rus, Filip (author), Dolžan, David (mentor)

V diplomskem delu predstavimo lastnosti vsote potenc in formule za njihov izračun. Najprej vsoto obravnavamo kot polinom spremenljivke n. Potem izpeljemo še formule za izračun vsote s Stirlingovimi števili druge vrste, Bernoullijevimi in Eulerjevimi števili ter za konec še rekurzivno formulo z integrali.

• Language: Slovenian
• Keywords: vsote potenc, polinom, Eulerjeva števila, Bernoullijeva števila, Stirlingova števila
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2022
• PID: 20.500.12556/RUL-139857
• UDC: 519.1
• COBISS.SI-ID: 120846339
• Publication date in RUL: 08.09.2022

Secondary language

• Language: English
• Title: Sums of powers of integers

Abstract

In this thesis we describe the characteristics of sums of powers and the formulas for their calculation. Firstly we focus on the sum as a polynomial in variable n. We also derive the formulas for calculating the sums of powers with Stirling numbers of the second kind, with Bernoulli numbers, and with Eulerian numbers. We end with recursive formula based on integration.

• Keywords: sums of powers of integers, polynomial, Eulerian numbers, Bernoulli numbers, Stirling numbers of the second kind