Some Double <i>q</i>-Series by Telescoping
By means of the telescoping method, we derived two general double series formulas that encapsulate the Riemann zeta values <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ζ</mi><mo>(&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/13/2949 |
| _version_ | 1797591197571612672 |
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| author | Kwang-Wu Chen |
| author_facet | Kwang-Wu Chen |
| author_sort | Kwang-Wu Chen |
| collection | DOAJ |
| description | By means of the telescoping method, we derived two general double series formulas that encapsulate the Riemann zeta values <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ζ</mi><mo>(</mo><mi>s</mi><mo>)</mo></mrow></semantics></math></inline-formula>, the Catalan constant <i>G</i>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>log</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> and several other significant mathematical constants. |
| first_indexed | 2024-03-11T01:35:05Z |
| format | Article |
| id | doaj.art-4ba45b57f8d94987aadcc22243586177 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T01:35:05Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4ba45b57f8d94987aadcc222435861772023-11-18T17:03:37ZengMDPI AGMathematics2227-73902023-07-011113294910.3390/math11132949Some Double <i>q</i>-Series by TelescopingKwang-Wu Chen0Department of Mathematics, University of Taipei, Taipei 100234, TaiwanBy means of the telescoping method, we derived two general double series formulas that encapsulate the Riemann zeta values <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ζ</mi><mo>(</mo><mi>s</mi><mo>)</mo></mrow></semantics></math></inline-formula>, the Catalan constant <i>G</i>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>log</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> and several other significant mathematical constants.https://www.mdpi.com/2227-7390/11/13/2949double series<i>q</i>-shifted factorial<i>q</i>-Gamma functionGaussian polynomial |
| spellingShingle | Kwang-Wu Chen Some Double <i>q</i>-Series by Telescoping Mathematics double series <i>q</i>-shifted factorial <i>q</i>-Gamma function Gaussian polynomial |
| title | Some Double <i>q</i>-Series by Telescoping |
| title_full | Some Double <i>q</i>-Series by Telescoping |
| title_fullStr | Some Double <i>q</i>-Series by Telescoping |
| title_full_unstemmed | Some Double <i>q</i>-Series by Telescoping |
| title_short | Some Double <i>q</i>-Series by Telescoping |
| title_sort | some double i q i series by telescoping |
| topic | double series <i>q</i>-shifted factorial <i>q</i>-Gamma function Gaussian polynomial |
| url | https://www.mdpi.com/2227-7390/11/13/2949 |
| work_keys_str_mv | AT kwangwuchen somedoubleiqiseriesbytelescoping |