Generalized Brouncker's continued fractions and their logarithmic derivatives
In this paper, we study the continued fraction y(s,r) which satisfies the equation y(s,r)y(s+2r,r)=(s+1)(s+2r-1) for r > 1/2. This continued fraction is a generalization of the Brouncker's continued fraction b(s). We extend the formulas for the first and the second logarithmic derivatives of...
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| creator | Kushel, O. Y |
| description | In this paper, we study the continued fraction y(s,r) which satisfies the
equation y(s,r)y(s+2r,r)=(s+1)(s+2r-1) for r > 1/2. This continued fraction is
a generalization of the Brouncker's continued fraction b(s). We extend the
formulas for the first and the second logarithmic derivatives of b(s) to the
case of y(s,r). The asymptotic series for y(s,r) at the infinity are also
studied. The generalizations of some Ramanujan's formulas are presented. |
| doi_str_mv | 10.48550/arxiv.1301.3734 |
| format | Article |
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equation y(s,r)y(s+2r,r)=(s+1)(s+2r-1) for r > 1/2. This continued fraction is
a generalization of the Brouncker's continued fraction b(s). We extend the
formulas for the first and the second logarithmic derivatives of b(s) to the
case of y(s,r). The asymptotic series for y(s,r) at the infinity are also
studied. The generalizations of some Ramanujan's formulas are presented.</description><identifier>DOI: 10.48550/arxiv.1301.3734</identifier><language>eng</language><subject>Mathematics - Number Theory</subject><creationdate>2013-01</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>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1301.3734$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1301.3734$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Kushel, O. Y</creatorcontrib><title>Generalized Brouncker's continued fractions and their logarithmic derivatives</title><description>In this paper, we study the continued fraction y(s,r) which satisfies the
equation y(s,r)y(s+2r,r)=(s+1)(s+2r-1) for r > 1/2. This continued fraction is
a generalization of the Brouncker's continued fraction b(s). We extend the
formulas for the first and the second logarithmic derivatives of b(s) to the
case of y(s,r). The asymptotic series for y(s,r) at the infinity are also
studied. The generalizations of some Ramanujan's formulas are presented.</description><subject>Mathematics - Number Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzz1PwzAUhWEvDKiwMyFvnRKcXH8kI1RQkIpYukeOfU2tpg66cSPg10Oh05He4UgPYzeVKGWjlLiz9BnnsgJRlWBAXrLXNSYkO8Rv9PyBxmNye6TlxN2YckzH3xrIuhzHNHGbPM87jMSH8d1SzLtDdNwjxdnmOON0xS6CHSa8Pu-CbZ8et6vnYvO2flndbwqrlSyCVK722kGLVW2Elw0GYXwvBQjpPTQGIehK97VxLdgG-laAUmB0r6AFAQt2-3_7x-k-KB4sfXUnVndiwQ9E8Ugb</recordid><startdate>20130116</startdate><enddate>20130116</enddate><creator>Kushel, O. Y</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20130116</creationdate><title>Generalized Brouncker's continued fractions and their logarithmic derivatives</title><author>Kushel, O. Y</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a654-f45c2d6c39e1270d48ef07db40304dd387e3f616b27c93a83b90355376b539303</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Mathematics - Number Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Kushel, O. Y</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Kushel, O. Y</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Generalized Brouncker's continued fractions and their logarithmic derivatives</atitle><date>2013-01-16</date><risdate>2013</risdate><abstract>In this paper, we study the continued fraction y(s,r) which satisfies the
equation y(s,r)y(s+2r,r)=(s+1)(s+2r-1) for r > 1/2. This continued fraction is
a generalization of the Brouncker's continued fraction b(s). We extend the
formulas for the first and the second logarithmic derivatives of b(s) to the
case of y(s,r). The asymptotic series for y(s,r) at the infinity are also
studied. The generalizations of some Ramanujan's formulas are presented.</abstract><doi>10.48550/arxiv.1301.3734</doi><oa>free_for_read</oa></addata></record> |
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| source | arXiv.org |
| subjects | Mathematics - Number Theory |
| title | Generalized Brouncker's continued fractions and their logarithmic derivatives |
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