On a problem due to Glasser on analytically tractable moments
Glasser, in 2011, introduced a remarkable integral identity of physical interest and suggested that the evaluation ∫ 0 1 / 2 k K 2 ( k ) d k = π G 4 provides the unique analytically tractable moment of K 2 on a sub-unit interval, where K denotes the complete elliptic integral of the first kind, and...
Gespeichert in:
Veröffentlicht in: | Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2024-03, Vol.57 (12), p.12 |
---|---|
1. Verfasser: | |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | |
---|---|
container_issue | 12 |
container_start_page | 12 |
container_title | Journal of physics. A, Mathematical and theoretical |
container_volume | 57 |
creator | Campbell, John M |
description | Glasser, in 2011, introduced a remarkable integral identity of physical interest and suggested that the evaluation
∫
0
1
/
2
k
K
2
(
k
)
d
k
=
π
G
4
provides the unique analytically tractable moment of
K
2
on a sub-unit interval, where
K
denotes the complete elliptic integral of the first kind, and where
G
=
1
1
2
−
1
3
2
+
1
5
2
−
⋯
denotes Catalan’s constant. We show how a case of Clausen’s product identity related to Ramanujan’s series for
1
π
may be applied, via an integration argument derived from our past work in fractional analysis and Fourier–Legendre theory, to show how higher moments of
K
2
on the same sub-unit interval may be evaluated analytically in terms of the Γ-function. This and Glasser’s moment formula are motivated by how closely related moment formulas for powers of
K
arise in the study of Feynman diagrams. |
doi_str_mv | 10.1088/1751-8121/ad2e3e |
format | Article |
fullrecord | <record><control><sourceid>iop_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1088_1751_8121_ad2e3e</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>aad2e3e</sourcerecordid><originalsourceid>FETCH-LOGICAL-c275t-85ac3f6701169a34022a4fb0f8cdcd279905027ca8f23c8e739efb77381b69503</originalsourceid><addsrcrecordid>eNp1j09LwzAYxoMoOKd3j_kA1r1J2iY9eJChUxjsoufwNk2go21Kkh367e2o7LbT-_A-f-BHyDODVwZKbZgsWKYYZxtsuBX2hqwur9uLZuKePMR4BChyqPiKvB0GinQMvu5sT5uTpcnTXYcx2kD97A3YTak12HUTTQFNwjlJe9_bIcVHcuewi_bp_67J7-fHz_Yr2x9239v3fWa4LFKmCjTClRIYKysUOXCOuavBKdOYhsuqggK4NKgcF0ZZKSrraimFYnVZFSDWBJZdE3yMwTo9hrbHMGkG-oyvz3z6zKoX_LnyslRaP-qjP4UZJF6P_wFvYVtE</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>On a problem due to Glasser on analytically tractable moments</title><source>Institute of Physics Journals</source><creator>Campbell, John M</creator><creatorcontrib>Campbell, John M</creatorcontrib><description>Glasser, in 2011, introduced a remarkable integral identity of physical interest and suggested that the evaluation
∫
0
1
/
2
k
K
2
(
k
)
d
k
=
π
G
4
provides the unique analytically tractable moment of
K
2
on a sub-unit interval, where
K
denotes the complete elliptic integral of the first kind, and where
G
=
1
1
2
−
1
3
2
+
1
5
2
−
⋯
denotes Catalan’s constant. We show how a case of Clausen’s product identity related to Ramanujan’s series for
1
π
may be applied, via an integration argument derived from our past work in fractional analysis and Fourier–Legendre theory, to show how higher moments of
K
2
on the same sub-unit interval may be evaluated analytically in terms of the Γ-function. This and Glasser’s moment formula are motivated by how closely related moment formulas for powers of
K
arise in the study of Feynman diagrams.</description><identifier>ISSN: 1751-8113</identifier><identifier>EISSN: 1751-8121</identifier><identifier>DOI: 10.1088/1751-8121/ad2e3e</identifier><identifier>CODEN: JPHAC5</identifier><language>eng</language><publisher>IOP Publishing</publisher><subject>complete elliptic integral ; Feynman diagram ; multiple elliptic integral</subject><ispartof>Journal of physics. A, Mathematical and theoretical, 2024-03, Vol.57 (12), p.12</ispartof><rights>2024 IOP Publishing Ltd</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c275t-85ac3f6701169a34022a4fb0f8cdcd279905027ca8f23c8e739efb77381b69503</cites><orcidid>0000-0001-5550-2938</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://iopscience.iop.org/article/10.1088/1751-8121/ad2e3e/pdf$$EPDF$$P50$$Giop$$H</linktopdf><link.rule.ids>314,780,784,27924,27925,53846,53893</link.rule.ids></links><search><creatorcontrib>Campbell, John M</creatorcontrib><title>On a problem due to Glasser on analytically tractable moments</title><title>Journal of physics. A, Mathematical and theoretical</title><addtitle>JPhysA</addtitle><addtitle>J. Phys. A: Math. Theor</addtitle><description>Glasser, in 2011, introduced a remarkable integral identity of physical interest and suggested that the evaluation
∫
0
1
/
2
k
K
2
(
k
)
d
k
=
π
G
4
provides the unique analytically tractable moment of
K
2
on a sub-unit interval, where
K
denotes the complete elliptic integral of the first kind, and where
G
=
1
1
2
−
1
3
2
+
1
5
2
−
⋯
denotes Catalan’s constant. We show how a case of Clausen’s product identity related to Ramanujan’s series for
1
π
may be applied, via an integration argument derived from our past work in fractional analysis and Fourier–Legendre theory, to show how higher moments of
K
2
on the same sub-unit interval may be evaluated analytically in terms of the Γ-function. This and Glasser’s moment formula are motivated by how closely related moment formulas for powers of
K
arise in the study of Feynman diagrams.</description><subject>complete elliptic integral</subject><subject>Feynman diagram</subject><subject>multiple elliptic integral</subject><issn>1751-8113</issn><issn>1751-8121</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp1j09LwzAYxoMoOKd3j_kA1r1J2iY9eJChUxjsoufwNk2go21Kkh367e2o7LbT-_A-f-BHyDODVwZKbZgsWKYYZxtsuBX2hqwur9uLZuKePMR4BChyqPiKvB0GinQMvu5sT5uTpcnTXYcx2kD97A3YTak12HUTTQFNwjlJe9_bIcVHcuewi_bp_67J7-fHz_Yr2x9239v3fWa4LFKmCjTClRIYKysUOXCOuavBKdOYhsuqggK4NKgcF0ZZKSrraimFYnVZFSDWBJZdE3yMwTo9hrbHMGkG-oyvz3z6zKoX_LnyslRaP-qjP4UZJF6P_wFvYVtE</recordid><startdate>20240322</startdate><enddate>20240322</enddate><creator>Campbell, John M</creator><general>IOP Publishing</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-5550-2938</orcidid></search><sort><creationdate>20240322</creationdate><title>On a problem due to Glasser on analytically tractable moments</title><author>Campbell, John M</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c275t-85ac3f6701169a34022a4fb0f8cdcd279905027ca8f23c8e739efb77381b69503</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>complete elliptic integral</topic><topic>Feynman diagram</topic><topic>multiple elliptic integral</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Campbell, John M</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of physics. A, Mathematical and theoretical</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Campbell, John M</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On a problem due to Glasser on analytically tractable moments</atitle><jtitle>Journal of physics. A, Mathematical and theoretical</jtitle><stitle>JPhysA</stitle><addtitle>J. Phys. A: Math. Theor</addtitle><date>2024-03-22</date><risdate>2024</risdate><volume>57</volume><issue>12</issue><spage>12</spage><pages>12-</pages><issn>1751-8113</issn><eissn>1751-8121</eissn><coden>JPHAC5</coden><abstract>Glasser, in 2011, introduced a remarkable integral identity of physical interest and suggested that the evaluation
∫
0
1
/
2
k
K
2
(
k
)
d
k
=
π
G
4
provides the unique analytically tractable moment of
K
2
on a sub-unit interval, where
K
denotes the complete elliptic integral of the first kind, and where
G
=
1
1
2
−
1
3
2
+
1
5
2
−
⋯
denotes Catalan’s constant. We show how a case of Clausen’s product identity related to Ramanujan’s series for
1
π
may be applied, via an integration argument derived from our past work in fractional analysis and Fourier–Legendre theory, to show how higher moments of
K
2
on the same sub-unit interval may be evaluated analytically in terms of the Γ-function. This and Glasser’s moment formula are motivated by how closely related moment formulas for powers of
K
arise in the study of Feynman diagrams.</abstract><pub>IOP Publishing</pub><doi>10.1088/1751-8121/ad2e3e</doi><tpages>7</tpages><orcidid>https://orcid.org/0000-0001-5550-2938</orcidid><oa>free_for_read</oa></addata></record> |
fulltext | fulltext |
identifier | ISSN: 1751-8113 |
ispartof | Journal of physics. A, Mathematical and theoretical, 2024-03, Vol.57 (12), p.12 |
issn | 1751-8113 1751-8121 |
language | eng |
recordid | cdi_crossref_primary_10_1088_1751_8121_ad2e3e |
source | Institute of Physics Journals |
subjects | complete elliptic integral Feynman diagram multiple elliptic integral |
title | On a problem due to Glasser on analytically tractable moments |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T12%3A06%3A27IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-iop_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20a%20problem%20due%20to%20Glasser%20on%20analytically%20tractable%20moments&rft.jtitle=Journal%20of%20physics.%20A,%20Mathematical%20and%20theoretical&rft.au=Campbell,%20John%20M&rft.date=2024-03-22&rft.volume=57&rft.issue=12&rft.spage=12&rft.pages=12-&rft.issn=1751-8113&rft.eissn=1751-8121&rft.coden=JPHAC5&rft_id=info:doi/10.1088/1751-8121/ad2e3e&rft_dat=%3Ciop_cross%3Eaad2e3e%3C/iop_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |