Möbius inversion formulae for Apostol-Bernoulli type polynomials and numbers
In this paper, we establish Möbius inversion formulae for the Fourier expansions of the Apostol-Bernoulli, Apostol-Euler and Apostol- Genocchi polynomials. As an application, by specializing our formulae at some special values we obtain interesting number-theoritical relations. We derive explicit fo...
Gespeichert in:
| Veröffentlicht in: | Mathematics of computation 2013-04, Vol.82 (284), p.2327-2332 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 2332 |
|---|---|
| container_issue | 284 |
| container_start_page | 2327 |
| container_title | Mathematics of computation |
| container_volume | 82 |
| creator | Bayad, A. Chikhi, J. |
| description | In this paper, we establish Möbius inversion formulae for the Fourier expansions of the Apostol-Bernoulli, Apostol-Euler and Apostol- Genocchi polynomials. As an application, by specializing our formulae at some special values we obtain interesting number-theoritical relations. We derive explicit formulae for Apostol-Bernoulli numbers. These formulae involve Stirling numbers of the second kind and powers of cotangent. Our proofs are very simple. |
| doi_str_mv | 10.1090/S0025-5718-2013-02699-3 |
| format | Article |
| fullrecord | <record><control><sourceid>jstor_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_04464014v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>42002743</jstor_id><sourcerecordid>42002743</sourcerecordid><originalsourceid>FETCH-LOGICAL-a405t-11214446a170499a813dd0afd4fb16a3c3f876b062e0e022d9e5299a3cea7ac43</originalsourceid><addsrcrecordid>eNqNkE1OwzAQRi0EEqVwBIS3LAwztvO3LAgoUisWwNpyEkekSuLIbir1YlyAi-E0qGtWM5r53rd4hNwg3CFkcP8OwCMWJZgyDigY8DjLmDghM4Q0ZXEq-SmZHUPn5ML7DQBgHCUzsl7_fOf14Gnd7Yzzte1oZV07NNqMC1301m9twx6M6-zQNDXd7ntDe9vsO9vWuvFUdyXthjYP-CU5q8LJXP3NOfl8fvp4XLLV28vr42LFtIRoyxA5SiljjQnILNMpirIEXZWyyjHWohBVmsQ5xNyAAc7LzEQ85ERhdKILKebkdur90o3qXd1qt1dW12q5WKnxBqFdAsodhmwyZQtnvXemOgIIajSoDgbVKEeNBtXBoBKBvJ7ITVDgjpjkIZ_I8c-nv279v0t_Adk8fNY</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Möbius inversion formulae for Apostol-Bernoulli type polynomials and numbers</title><source>Jstor Complete Legacy</source><source>American Mathematical Society Publications</source><source>American Mathematical Society Publications (Freely Accessible)</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>JSTOR Mathematics & Statistics</source><creator>Bayad, A. ; Chikhi, J.</creator><creatorcontrib>Bayad, A. ; Chikhi, J.</creatorcontrib><description>In this paper, we establish Möbius inversion formulae for the Fourier expansions of the Apostol-Bernoulli, Apostol-Euler and Apostol- Genocchi polynomials. As an application, by specializing our formulae at some special values we obtain interesting number-theoritical relations. We derive explicit formulae for Apostol-Bernoulli numbers. These formulae involve Stirling numbers of the second kind and powers of cotangent. Our proofs are very simple.</description><identifier>ISSN: 0025-5718</identifier><identifier>EISSN: 1088-6842</identifier><identifier>DOI: 10.1090/S0025-5718-2013-02699-3</identifier><language>eng</language><publisher>Providence, Rhode Island: American Mathematical Society</publisher><subject>Fourier series ; Integers ; Mathematical functions ; Mathematical theorems ; Mathematics ; Number Theory ; Numbers ; Polynomials ; Research article</subject><ispartof>Mathematics of computation, 2013-04, Vol.82 (284), p.2327-2332</ispartof><rights>Copyright 2013 American Mathematical Society; reverts to public domain 28 years from publication</rights><rights>2013 American Mathematical Society</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a405t-11214446a170499a813dd0afd4fb16a3c3f876b062e0e022d9e5299a3cea7ac43</citedby><orcidid>0000-0002-8003-335X ; 0000-0002-0867-8305</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.ams.org/mcom/2013-82-284/S0025-5718-2013-02699-3/S0025-5718-2013-02699-3.pdf$$EPDF$$P50$$Gams$$H</linktopdf><linktohtml>$$Uhttps://www.ams.org/mcom/2013-82-284/S0025-5718-2013-02699-3/$$EHTML$$P50$$Gams$$H</linktohtml><link.rule.ids>68,69,230,314,776,780,799,828,881,23303,23307,27901,27902,57992,57996,58225,58229,77805,77807,77815,77817</link.rule.ids><backlink>$$Uhttps://hal.science/hal-04464014$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Bayad, A.</creatorcontrib><creatorcontrib>Chikhi, J.</creatorcontrib><title>Möbius inversion formulae for Apostol-Bernoulli type polynomials and numbers</title><title>Mathematics of computation</title><addtitle>Math. Comp</addtitle><description>In this paper, we establish Möbius inversion formulae for the Fourier expansions of the Apostol-Bernoulli, Apostol-Euler and Apostol- Genocchi polynomials. As an application, by specializing our formulae at some special values we obtain interesting number-theoritical relations. We derive explicit formulae for Apostol-Bernoulli numbers. These formulae involve Stirling numbers of the second kind and powers of cotangent. Our proofs are very simple.</description><subject>Fourier series</subject><subject>Integers</subject><subject>Mathematical functions</subject><subject>Mathematical theorems</subject><subject>Mathematics</subject><subject>Number Theory</subject><subject>Numbers</subject><subject>Polynomials</subject><subject>Research article</subject><issn>0025-5718</issn><issn>1088-6842</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNqNkE1OwzAQRi0EEqVwBIS3LAwztvO3LAgoUisWwNpyEkekSuLIbir1YlyAi-E0qGtWM5r53rd4hNwg3CFkcP8OwCMWJZgyDigY8DjLmDghM4Q0ZXEq-SmZHUPn5ML7DQBgHCUzsl7_fOf14Gnd7Yzzte1oZV07NNqMC1301m9twx6M6-zQNDXd7ntDe9vsO9vWuvFUdyXthjYP-CU5q8LJXP3NOfl8fvp4XLLV28vr42LFtIRoyxA5SiljjQnILNMpirIEXZWyyjHWohBVmsQ5xNyAAc7LzEQ85ERhdKILKebkdur90o3qXd1qt1dW12q5WKnxBqFdAsodhmwyZQtnvXemOgIIajSoDgbVKEeNBtXBoBKBvJ7ITVDgjpjkIZ_I8c-nv279v0t_Adk8fNY</recordid><startdate>20130424</startdate><enddate>20130424</enddate><creator>Bayad, A.</creator><creator>Chikhi, J.</creator><general>American Mathematical Society</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-8003-335X</orcidid><orcidid>https://orcid.org/0000-0002-0867-8305</orcidid></search><sort><creationdate>20130424</creationdate><title>Möbius inversion formulae for Apostol-Bernoulli type polynomials and numbers</title><author>Bayad, A. ; Chikhi, J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a405t-11214446a170499a813dd0afd4fb16a3c3f876b062e0e022d9e5299a3cea7ac43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Fourier series</topic><topic>Integers</topic><topic>Mathematical functions</topic><topic>Mathematical theorems</topic><topic>Mathematics</topic><topic>Number Theory</topic><topic>Numbers</topic><topic>Polynomials</topic><topic>Research article</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bayad, A.</creatorcontrib><creatorcontrib>Chikhi, J.</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Mathematics of computation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bayad, A.</au><au>Chikhi, J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Möbius inversion formulae for Apostol-Bernoulli type polynomials and numbers</atitle><jtitle>Mathematics of computation</jtitle><stitle>Math. Comp</stitle><date>2013-04-24</date><risdate>2013</risdate><volume>82</volume><issue>284</issue><spage>2327</spage><epage>2332</epage><pages>2327-2332</pages><issn>0025-5718</issn><eissn>1088-6842</eissn><abstract>In this paper, we establish Möbius inversion formulae for the Fourier expansions of the Apostol-Bernoulli, Apostol-Euler and Apostol- Genocchi polynomials. As an application, by specializing our formulae at some special values we obtain interesting number-theoritical relations. We derive explicit formulae for Apostol-Bernoulli numbers. These formulae involve Stirling numbers of the second kind and powers of cotangent. Our proofs are very simple.</abstract><cop>Providence, Rhode Island</cop><pub>American Mathematical Society</pub><doi>10.1090/S0025-5718-2013-02699-3</doi><tpages>6</tpages><orcidid>https://orcid.org/0000-0002-8003-335X</orcidid><orcidid>https://orcid.org/0000-0002-0867-8305</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0025-5718 |
| ispartof | Mathematics of computation, 2013-04, Vol.82 (284), p.2327-2332 |
| issn | 0025-5718 1088-6842 |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_hal_04464014v1 |
| source | Jstor Complete Legacy; American Mathematical Society Publications; American Mathematical Society Publications (Freely Accessible); Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; JSTOR Mathematics & Statistics |
| subjects | Fourier series Integers Mathematical functions Mathematical theorems Mathematics Number Theory Numbers Polynomials Research article |
| title | Möbius inversion formulae for Apostol-Bernoulli type polynomials and numbers |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-13T16%3A05%3A10IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_hal_p&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=M%C3%B6bius%20inversion%20formulae%20for%20Apostol-Bernoulli%20type%20polynomials%20and%20numbers&rft.jtitle=Mathematics%20of%20computation&rft.au=Bayad,%20A.&rft.date=2013-04-24&rft.volume=82&rft.issue=284&rft.spage=2327&rft.epage=2332&rft.pages=2327-2332&rft.issn=0025-5718&rft.eissn=1088-6842&rft_id=info:doi/10.1090/S0025-5718-2013-02699-3&rft_dat=%3Cjstor_hal_p%3E42002743%3C/jstor_hal_p%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_jstor_id=42002743&rfr_iscdi=true |