Applications of derivative and difference operators on some sequences
In this study, depending on the upper and the lower indices of the hyperharmonic number $h_{n}^{(r)}$, nonlinear recurrence relations are obtained. It is shown that generalized harmonic number and hyperharmonic number can be obtained from derivatives of the binomial coefficients. Taking into account...
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| creator | Dil, Ayhan Muniroğlu, Erkan |
| description | In this study, depending on the upper and the lower indices of the
hyperharmonic number $h_{n}^{(r)}$, nonlinear recurrence relations are
obtained. It is shown that generalized harmonic number and hyperharmonic number
can be obtained from derivatives of the binomial coefficients. Taking into
account of difference and derivative operators, several identities of the
harmonic and hyperharmonic numbers are given. Negative-ordered hyperharmonic
number is defined and its alternative representations are given. |
| doi_str_mv | 10.48550/arxiv.1910.01876 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_1910_01876</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1910_01876</sourcerecordid><originalsourceid>FETCH-LOGICAL-a676-873299ce308a5ccb929e730d2a79650d9790b88c502fbcdddf3e14e381b7217d3</originalsourceid><addsrcrecordid>eNotj8tqAjEUhrNxUWwfoCvzAmNzMZNkKWIvIHTjfjiTcwIBnUwTHdq372i7-vkv_PAx9izFeuOMES9QvtO0ln4OhHS2fWD77TieUoBLykPlOXKkkqbZTsRhQI4pRio0BOJ5pAKXXObZwGs-E6_0db1V9ZEtIpwqPf3rkh1f98fde3P4fPvYbQ8NtLZtnNXK-0BaODAh9F55slqgAutbI9BbL3rnghEq9gERoya5Ie1kb5W0qJds9Xd75-jGks5QfrobT3fn0b8IZkYe</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Applications of derivative and difference operators on some sequences</title><source>arXiv.org</source><creator>Dil, Ayhan ; Muniroğlu, Erkan</creator><creatorcontrib>Dil, Ayhan ; Muniroğlu, Erkan</creatorcontrib><description>In this study, depending on the upper and the lower indices of the
hyperharmonic number $h_{n}^{(r)}$, nonlinear recurrence relations are
obtained. It is shown that generalized harmonic number and hyperharmonic number
can be obtained from derivatives of the binomial coefficients. Taking into
account of difference and derivative operators, several identities of the
harmonic and hyperharmonic numbers are given. Negative-ordered hyperharmonic
number is defined and its alternative representations are given.</description><identifier>DOI: 10.48550/arxiv.1910.01876</identifier><language>eng</language><subject>Mathematics - Classical Analysis and ODEs ; Mathematics - Combinatorics ; Mathematics - Number Theory</subject><creationdate>2019-10</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1910.01876$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1910.01876$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Dil, Ayhan</creatorcontrib><creatorcontrib>Muniroğlu, Erkan</creatorcontrib><title>Applications of derivative and difference operators on some sequences</title><description>In this study, depending on the upper and the lower indices of the
hyperharmonic number $h_{n}^{(r)}$, nonlinear recurrence relations are
obtained. It is shown that generalized harmonic number and hyperharmonic number
can be obtained from derivatives of the binomial coefficients. Taking into
account of difference and derivative operators, several identities of the
harmonic and hyperharmonic numbers are given. Negative-ordered hyperharmonic
number is defined and its alternative representations are given.</description><subject>Mathematics - Classical Analysis and ODEs</subject><subject>Mathematics - Combinatorics</subject><subject>Mathematics - Number Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8tqAjEUhrNxUWwfoCvzAmNzMZNkKWIvIHTjfjiTcwIBnUwTHdq372i7-vkv_PAx9izFeuOMES9QvtO0ln4OhHS2fWD77TieUoBLykPlOXKkkqbZTsRhQI4pRio0BOJ5pAKXXObZwGs-E6_0db1V9ZEtIpwqPf3rkh1f98fde3P4fPvYbQ8NtLZtnNXK-0BaODAh9F55slqgAutbI9BbL3rnghEq9gERoya5Ie1kb5W0qJds9Xd75-jGks5QfrobT3fn0b8IZkYe</recordid><startdate>20191004</startdate><enddate>20191004</enddate><creator>Dil, Ayhan</creator><creator>Muniroğlu, Erkan</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20191004</creationdate><title>Applications of derivative and difference operators on some sequences</title><author>Dil, Ayhan ; Muniroğlu, Erkan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a676-873299ce308a5ccb929e730d2a79650d9790b88c502fbcdddf3e14e381b7217d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Mathematics - Classical Analysis and ODEs</topic><topic>Mathematics - Combinatorics</topic><topic>Mathematics - Number Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Dil, Ayhan</creatorcontrib><creatorcontrib>Muniroğlu, Erkan</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Dil, Ayhan</au><au>Muniroğlu, Erkan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Applications of derivative and difference operators on some sequences</atitle><date>2019-10-04</date><risdate>2019</risdate><abstract>In this study, depending on the upper and the lower indices of the
hyperharmonic number $h_{n}^{(r)}$, nonlinear recurrence relations are
obtained. It is shown that generalized harmonic number and hyperharmonic number
can be obtained from derivatives of the binomial coefficients. Taking into
account of difference and derivative operators, several identities of the
harmonic and hyperharmonic numbers are given. Negative-ordered hyperharmonic
number is defined and its alternative representations are given.</abstract><doi>10.48550/arxiv.1910.01876</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Classical Analysis and ODEs Mathematics - Combinatorics Mathematics - Number Theory |
| title | Applications of derivative and difference operators on some sequences |
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