SOME IMPROPER INTEGRALS INVOLVING THE SQUARE OF THE TAIL OF THE SINE AND COSINE FUNCTIONS

Seán M. Stewart

doi:10.7153/jca-2020-16-10

SOME IMPROPER INTEGRALS INVOLVING THE SQUARE OF THE TAIL OF THE SINE AND COSINE FUNCTIONS

Seán M. Stewart^*

^*Corresponding author for this work

Physical Sciences and Engineering

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

3 Scopus citations

Abstract

A class of four improper integrals containing the square of the tail of the sine and cosine functions in their integrand are found using Fourier transform methods. Relations between the four improper integrals considered are given and an open problem concerning the general form of certain improper integrals of this type is raised.

Original language	English (US)
Pages (from-to)	91-99
Number of pages	9
Journal	Journal of Classical Analysis
Volume	16
Issue number	2
DOIs	https://doi.org/10.7153/jca-2020-16-10
State	Published - Apr 2020

Keywords

binomial identity
Fourier transform
Improper integral
Laplace transform

ASJC Scopus subject areas

Analysis
Statistics and Probability

Access to Document

10.7153/jca-2020-16-10

Cite this

@article{55200637d2ce4c748e3166210cc9b9fc,

title = "SOME IMPROPER INTEGRALS INVOLVING THE SQUARE OF THE TAIL OF THE SINE AND COSINE FUNCTIONS",

abstract = "A class of four improper integrals containing the square of the tail of the sine and cosine functions in their integrand are found using Fourier transform methods. Relations between the four improper integrals considered are given and an open problem concerning the general form of certain improper integrals of this type is raised.",

keywords = "binomial identity, Fourier transform, Improper integral, Laplace transform",

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

year = "2020",

month = apr,

doi = "10.7153/jca-2020-16-10",

language = "English (US)",

volume = "16",

pages = "91--99",

journal = "Journal of Classical Analysis",

issn = "1848-5987",

publisher = "Ele-Math",

number = "2",

}

TY - JOUR

T1 - SOME IMPROPER INTEGRALS INVOLVING THE SQUARE OF THE TAIL OF THE SINE AND COSINE FUNCTIONS

AU - Stewart, Seán M.

PY - 2020/4

Y1 - 2020/4

N2 - A class of four improper integrals containing the square of the tail of the sine and cosine functions in their integrand are found using Fourier transform methods. Relations between the four improper integrals considered are given and an open problem concerning the general form of certain improper integrals of this type is raised.

AB - A class of four improper integrals containing the square of the tail of the sine and cosine functions in their integrand are found using Fourier transform methods. Relations between the four improper integrals considered are given and an open problem concerning the general form of certain improper integrals of this type is raised.

KW - binomial identity

KW - Fourier transform

KW - Improper integral

KW - Laplace transform

UR - http://www.scopus.com/inward/record.url?scp=85148625418&partnerID=8YFLogxK

U2 - 10.7153/jca-2020-16-10

DO - 10.7153/jca-2020-16-10

M3 - Article

AN - SCOPUS:85148625418

SN - 1848-5987

VL - 16

SP - 91

EP - 99

JO - Journal of Classical Analysis

JF - Journal of Classical Analysis

IS - 2

ER -

SOME IMPROPER INTEGRALS INVOLVING THE SQUARE OF THE TAIL OF THE SINE AND COSINE FUNCTIONS

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this