Tighter bounds for the inequalities of Sinc function based on reparameterization
In this article, a new refined inequality containing trigonometric function for sinc function is established, which is based on the reparameterization technique. It utilizes the help of computer for proving the main results. It also provides two-sided bounds of sin ( x ) x λ for the cases that λ ∈ (...
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| Veröffentlicht in: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2022, Vol.116 (1), Article 29 |
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| container_title | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas |
| container_volume | 116 |
| creator | Qian, Cheng Chen, Xiao-Diao Malesevic, Branko |
| description | In this article, a new refined inequality containing trigonometric function for sinc function is established, which is based on the reparameterization technique. It utilizes the help of computer for proving the main results. It also provides two-sided bounds of
sin
(
x
)
x
λ
for the cases that
λ
∈
(
1
,
4
)
, which makes up for the leak that there is no two-sided bounds of
sin
(
x
)
x
λ
for the cases that
λ
∈
7
5
,
3
-
π
2
. Numerical examples show that the new results achieves much tighter bounds than those of prevailing methods for sinc function. |
| doi_str_mv | 10.1007/s13398-021-01170-9 |
| format | Article |
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sin
(
x
)
x
λ
for the cases that
λ
∈
(
1
,
4
)
, which makes up for the leak that there is no two-sided bounds of
sin
(
x
)
x
λ
for the cases that
λ
∈
7
5
,
3
-
π
2
. Numerical examples show that the new results achieves much tighter bounds than those of prevailing methods for sinc function.</description><identifier>ISSN: 1578-7303</identifier><identifier>EISSN: 1579-1505</identifier><identifier>DOI: 10.1007/s13398-021-01170-9</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Applications of Mathematics ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Original Paper ; Theoretical ; Trigonometric functions</subject><ispartof>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 2022, Vol.116 (1), Article 29</ispartof><rights>The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2021</rights><rights>The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-62f167fe22b7a28ac85d9353ffcb04f2337c919fb97fd805b400caaac37a49dc3</citedby><cites>FETCH-LOGICAL-c319t-62f167fe22b7a28ac85d9353ffcb04f2337c919fb97fd805b400caaac37a49dc3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s13398-021-01170-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s13398-021-01170-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Qian, Cheng</creatorcontrib><creatorcontrib>Chen, Xiao-Diao</creatorcontrib><creatorcontrib>Malesevic, Branko</creatorcontrib><title>Tighter bounds for the inequalities of Sinc function based on reparameterization</title><title>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas</title><addtitle>RACSAM</addtitle><description>In this article, a new refined inequality containing trigonometric function for sinc function is established, which is based on the reparameterization technique. It utilizes the help of computer for proving the main results. It also provides two-sided bounds of
sin
(
x
)
x
λ
for the cases that
λ
∈
(
1
,
4
)
, which makes up for the leak that there is no two-sided bounds of
sin
(
x
)
x
λ
for the cases that
λ
∈
7
5
,
3
-
π
2
. Numerical examples show that the new results achieves much tighter bounds than those of prevailing methods for sinc function.</description><subject>Applications of Mathematics</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Theoretical</subject><subject>Trigonometric functions</subject><issn>1578-7303</issn><issn>1579-1505</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LAzEQxYMoWLRfwFPAc3SSbJrNUYr_oKBgPYdsNmlT2myb7B7005t2BW_OZR7Me2_gh9ANhTsKIO8z5VzVBBglQKkEos7QhAqpCBUgzk-6JpIDv0TTnDdQhtOqBjlB78uwWvcu4aYbYpux7xLu1w6H6A6D2YY-uIw7jz9CtNgP0fahi7gx2bW4iOT2JpmdKw3h2xxv1-jCm2120999hT6fHpfzF7J4e36dPyyI5VT1ZMY8nUnvGGukYbWxtWgVF9x720DlGefSKqp8o6RvaxBNBWCNMZZLU6nW8it0O_buU3cYXO71phtSLC81E_VMAJWcFhcbXTZ1OSfn9T6FnUlfmoI-wtMjPF3g6RM8rUqIj6FczHHl0l_1P6kfyRpyhw</recordid><startdate>2022</startdate><enddate>2022</enddate><creator>Qian, Cheng</creator><creator>Chen, Xiao-Diao</creator><creator>Malesevic, Branko</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>2022</creationdate><title>Tighter bounds for the inequalities of Sinc function based on reparameterization</title><author>Qian, Cheng ; Chen, Xiao-Diao ; Malesevic, Branko</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-62f167fe22b7a28ac85d9353ffcb04f2337c919fb97fd805b400caaac37a49dc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Applications of Mathematics</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Theoretical</topic><topic>Trigonometric functions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Qian, Cheng</creatorcontrib><creatorcontrib>Chen, Xiao-Diao</creatorcontrib><creatorcontrib>Malesevic, Branko</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Qian, Cheng</au><au>Chen, Xiao-Diao</au><au>Malesevic, Branko</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Tighter bounds for the inequalities of Sinc function based on reparameterization</atitle><jtitle>Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas</jtitle><stitle>RACSAM</stitle><date>2022</date><risdate>2022</risdate><volume>116</volume><issue>1</issue><artnum>29</artnum><issn>1578-7303</issn><eissn>1579-1505</eissn><abstract>In this article, a new refined inequality containing trigonometric function for sinc function is established, which is based on the reparameterization technique. It utilizes the help of computer for proving the main results. It also provides two-sided bounds of
sin
(
x
)
x
λ
for the cases that
λ
∈
(
1
,
4
)
, which makes up for the leak that there is no two-sided bounds of
sin
(
x
)
x
λ
for the cases that
λ
∈
7
5
,
3
-
π
2
. Numerical examples show that the new results achieves much tighter bounds than those of prevailing methods for sinc function.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s13398-021-01170-9</doi></addata></record> |
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| ispartof | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 2022, Vol.116 (1), Article 29 |
| issn | 1578-7303 1579-1505 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Applications of Mathematics Mathematical and Computational Physics Mathematics Mathematics and Statistics Original Paper Theoretical Trigonometric functions |
| title | Tighter bounds for the inequalities of Sinc function based on reparameterization |
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