Iterated integrals of polynomials

Edyta Hetmaniok; Piotr Lorenc; Mariusz Pleszczyński; Roman Wituła

doi:10.1016/j.amc.2014.10.057

Iterated integrals of polynomials

Silesian University of Technology

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

The paper concerns the decompositions of polynomials onto iterated integrals. This is a continuation of our previous paper (Lorenc, submitted for publication), in which the existence of such decomposition for the Faulhaber polynomials is proven. In the current paper we prove the basic theorem (Theorem 2) presenting the necessary and sufficient conditions for the existence of such decomposition. We discuss these conditions in the wider context of theory of the real and complex polynomials. A number of exemplary decompositions onto iterated integrals of the known classical kinds of polynomials are also presented.

Original language	English
Pages (from-to)	389-398
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	249
DOIs	https://doi.org/10.1016/j.amc.2014.10.057
Publication status	Published - 15 Dec 2014

Keywords

Hyperbolic polynomials
Iterated polynomials
Real polynomials

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2014.10.057

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title = "Iterated integrals of polynomials",

abstract = "The paper concerns the decompositions of polynomials onto iterated integrals. This is a continuation of our previous paper (Lorenc, submitted for publication), in which the existence of such decomposition for the Faulhaber polynomials is proven. In the current paper we prove the basic theorem (Theorem 2) presenting the necessary and sufficient conditions for the existence of such decomposition. We discuss these conditions in the wider context of theory of the real and complex polynomials. A number of exemplary decompositions onto iterated integrals of the known classical kinds of polynomials are also presented.",

keywords = "Hyperbolic polynomials, Iterated polynomials, Real polynomials",

author = "Edyta Hetmaniok and Piotr Lorenc and Mariusz Pleszczy{\'n}ski and Roman Witu{\l}a",

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T1 - Iterated integrals of polynomials

AU - Hetmaniok, Edyta

AU - Lorenc, Piotr

AU - Pleszczyński, Mariusz

AU - Wituła, Roman

PY - 2014/12/15

Y1 - 2014/12/15

N2 - The paper concerns the decompositions of polynomials onto iterated integrals. This is a continuation of our previous paper (Lorenc, submitted for publication), in which the existence of such decomposition for the Faulhaber polynomials is proven. In the current paper we prove the basic theorem (Theorem 2) presenting the necessary and sufficient conditions for the existence of such decomposition. We discuss these conditions in the wider context of theory of the real and complex polynomials. A number of exemplary decompositions onto iterated integrals of the known classical kinds of polynomials are also presented.

AB - The paper concerns the decompositions of polynomials onto iterated integrals. This is a continuation of our previous paper (Lorenc, submitted for publication), in which the existence of such decomposition for the Faulhaber polynomials is proven. In the current paper we prove the basic theorem (Theorem 2) presenting the necessary and sufficient conditions for the existence of such decomposition. We discuss these conditions in the wider context of theory of the real and complex polynomials. A number of exemplary decompositions onto iterated integrals of the known classical kinds of polynomials are also presented.

KW - Hyperbolic polynomials

KW - Iterated polynomials

KW - Real polynomials

UR - https://www.scopus.com/pages/publications/84910068465

U2 - 10.1016/j.amc.2014.10.057

DO - 10.1016/j.amc.2014.10.057

M3 - Article

AN - SCOPUS:84910068465

SN - 0096-3003

VL - 249

SP - 389

EP - 398

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Iterated integrals of polynomials

Abstract

Keywords

ASJC Scopus subject areas

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