π-Formulas from Dual Series of the Dougall Theorem
By means of the extended Gould–Hsu inverse series relations, we show that the dual relation of Dougall’s summation theorem for a well-poised 7 F 6 -series can be used to construct numerous interesting Ramanujanlike infinite-series expressions for π ± 1 and π ± 2 , including an elegant formula for π...
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| Veröffentlicht in: | Ukrainian mathematical journal 2023-05, Vol.74 (12), p.1924-1949 |
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| container_end_page | 1949 |
|---|---|
| container_issue | 12 |
| container_start_page | 1924 |
| container_title | Ukrainian mathematical journal |
| container_volume | 74 |
| creator | Chu, W. |
| description | By means of the extended Gould–Hsu inverse series relations, we show that the dual relation of Dougall’s summation theorem for a well-poised
7
F
6
-series can be used to construct numerous interesting Ramanujanlike infinite-series expressions for π
±
1
and π
±
2
,
including an elegant formula for π
−
2
due to Guillera. |
| doi_str_mv | 10.1007/s11253-023-02179-6 |
| format | Article |
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7
F
6
-series can be used to construct numerous interesting Ramanujanlike infinite-series expressions for π
±
1
and π
±
2
,
including an elegant formula for π
−
2
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7
F
6
-series can be used to construct numerous interesting Ramanujanlike infinite-series expressions for π
±
1
and π
±
2
,
including an elegant formula for π
−
2
due to Guillera.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Formulas (mathematics)</subject><subject>Geometry</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Statistics</subject><subject>Theorems</subject><issn>0041-5995</issn><issn>1573-9376</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kLlOAzEURS0EEiHwA1SWqA1exluJEgJIkSgIteXMPGfRTBzsTEHHH_JLOAwSHcXTbe65TzoIXTN6yyjVd5kxLgWh_HhMW6JO0IhJLYgVWp2iEaUVI9JaeY4uct5SWjCjR0h8fZJZTF3f-oxDih2e9r7Fr5A2kHEM-LAGPI39yrctXqwhJugu0VnwbYar3xyjt9nDYvJE5i-Pz5P7Oam5pgcCVgRQnlIljVK2MkvOWOO5tVbwuqmZMrVgWoKkwQMzXlS8kaERUHEjl0sxRjfD7j7F9x7ywW1jn3blpeNGKFtmhSktPrTqFHNOENw-bTqfPhyj7ijHDXJckeN-5DhVIDFAuZR3K0h_0_9Q39AZZX8</recordid><startdate>20230501</startdate><enddate>20230501</enddate><creator>Chu, W.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20230501</creationdate><title>π-Formulas from Dual Series of the Dougall Theorem</title><author>Chu, W.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-e93fe6a0065866948b211da299932cdc168c3175e50fae18a342d5fd3e4285bb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Formulas (mathematics)</topic><topic>Geometry</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Statistics</topic><topic>Theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chu, W.</creatorcontrib><collection>CrossRef</collection><jtitle>Ukrainian mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chu, W.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>π-Formulas from Dual Series of the Dougall Theorem</atitle><jtitle>Ukrainian mathematical journal</jtitle><stitle>Ukr Math J</stitle><date>2023-05-01</date><risdate>2023</risdate><volume>74</volume><issue>12</issue><spage>1924</spage><epage>1949</epage><pages>1924-1949</pages><issn>0041-5995</issn><eissn>1573-9376</eissn><abstract>By means of the extended Gould–Hsu inverse series relations, we show that the dual relation of Dougall’s summation theorem for a well-poised
7
F
6
-series can be used to construct numerous interesting Ramanujanlike infinite-series expressions for π
±
1
and π
±
2
,
including an elegant formula for π
−
2
due to Guillera.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11253-023-02179-6</doi><tpages>26</tpages></addata></record> |
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| identifier | ISSN: 0041-5995 |
| ispartof | Ukrainian mathematical journal, 2023-05, Vol.74 (12), p.1924-1949 |
| issn | 0041-5995 1573-9376 |
| language | eng |
| recordid | cdi_proquest_journals_2836958638 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Algebra Analysis Applications of Mathematics Formulas (mathematics) Geometry Mathematics Mathematics and Statistics Statistics Theorems |
| title | π-Formulas from Dual Series of the Dougall Theorem |
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