The iterated integrals of ln(1+x^n)

Tewodros Amdeberhan; Christoph Koutschan; Victor H. Moll; Eric S. Rowland

doi:10.1142/S1793042112500042

The iterated integrals of ln(1+x^n)

Tewodros Amdeberhan
, Christoph Koutschan
, Victor H. Moll
, Eric S. Rowland

Research Institute for Symbolic Computation

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

Abstract

For a polynomial P, we consider the sequence of iterated integrals of ln P(x). This sequence is expressed in terms of the zeros of P(x). In the special case of ln(1+x^2 ), arithmetic properties of certain coefficients arising are described. Similar observations are made for ln(1+x^3).

Original language	English
Pages (from-to)	71-94
Number of pages	24
Journal	International Journal of Number Theory
Volume	8
Issue number	1
DOIs	https://doi.org/10.1142/S1793042112500042
Publication status	Published - Feb 2012

Fields of science

101001 Algebra
101002 Analysis
101 Mathematics
102 Computer Sciences
102011 Formal languages
101009 Geometry
101013 Mathematical logic
101020 Technical mathematics
101025 Number theory
101012 Combinatorics
101005 Computer algebra
101006 Differential geometry
101003 Applied geometry
102025 Distributed systems

JKU Focus areas

Computation in Informatics and Mathematics

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10.1142/S1793042112500042

Cite this

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title = "The iterated integrals of ln(1+x\textasciicircum{}n)",

abstract = "For a polynomial P, we consider the sequence of iterated integrals of ln P(x). This sequence is expressed in terms of the zeros of P(x). In the special case of ln(1+x\textasciicircum{}2 ), arithmetic properties of certain coefficients arising are described. Similar observations are made for ln(1+x\textasciicircum{}3).",

author = "Tewodros Amdeberhan and Christoph Koutschan and Moll, \{Victor H.\} and Rowland, \{Eric S.\}",

year = "2012",

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doi = "10.1142/S1793042112500042",

language = "English",

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pages = "71--94",

journal = "International Journal of Number Theory",

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publisher = "World Scientific",

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T1 - The iterated integrals of ln(1+x^n)

AU - Amdeberhan, Tewodros

AU - Koutschan, Christoph

AU - Moll, Victor H.

AU - Rowland, Eric S.

PY - 2012/2

Y1 - 2012/2

N2 - For a polynomial P, we consider the sequence of iterated integrals of ln P(x). This sequence is expressed in terms of the zeros of P(x). In the special case of ln(1+x^2 ), arithmetic properties of certain coefficients arising are described. Similar observations are made for ln(1+x^3).

AB - For a polynomial P, we consider the sequence of iterated integrals of ln P(x). This sequence is expressed in terms of the zeros of P(x). In the special case of ln(1+x^2 ), arithmetic properties of certain coefficients arising are described. Similar observations are made for ln(1+x^3).

UR - https://www.scopus.com/pages/publications/84856609811

U2 - 10.1142/S1793042112500042

DO - 10.1142/S1793042112500042

M3 - Article

SN - 1793-0421

VL - 8

SP - 71

EP - 94

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 1

ER -

The iterated integrals of ln(1+x^n)

Abstract

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