A POISSON LOGARITHMIC INTEGRAL FOR INTEGER ORDER POWERS n = 0, 1, 2, AND 3

Seán M. Stewart

doi:10.7153/jca-2021-17-01

A POISSON LOGARITHMIC INTEGRAL FOR INTEGER ORDER POWERS n = 0, 1, 2, AND 3

Seán M. Stewart^*

^*Corresponding author for this work

Physical Sciences and Engineering

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

Abstract

We give analytic expressions for the Poisson type logarithmic integral [formula presented] for integer order powers n = 0,1,2, and 3. Here a is any real number. A generalisation of the integral for the n = 2 case is also given.

Original language	English (US)
Pages (from-to)	1-11
Number of pages	11
Journal	Journal of Classical Analysis
Volume	17
Issue number	1
DOIs	https://doi.org/10.7153/jca-2021-17-01
State	Published - Jan 2021

Keywords

Euler sums
log-sine integral
Poisson integral
polylogarithm

ASJC Scopus subject areas

Analysis
Statistics and Probability

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10.7153/jca-2021-17-01

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title = "A POISSON LOGARITHMIC INTEGRAL FOR INTEGER ORDER POWERS n = 0, 1, 2, AND 3",

abstract = "We give analytic expressions for the Poisson type logarithmic integral [formula presented] for integer order powers n = 0,1,2, and 3. Here a is any real number. A generalisation of the integral for the n = 2 case is also given.",

keywords = "Euler sums, log-sine integral, Poisson integral, polylogarithm",

author = "Stewart, {Se{\'a}n M.}",

year = "2021",

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doi = "10.7153/jca-2021-17-01",

language = "English (US)",

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AB - We give analytic expressions for the Poisson type logarithmic integral [formula presented] for integer order powers n = 0,1,2, and 3. Here a is any real number. A generalisation of the integral for the n = 2 case is also given.

KW - Euler sums

KW - log-sine integral

KW - Poisson integral

KW - polylogarithm

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A POISSON LOGARITHMIC INTEGRAL FOR INTEGER ORDER POWERS n = 0, 1, 2, AND 3

Abstract

Keywords

ASJC Scopus subject areas

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