<i>q</i>-Analogs of <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold-italic">H</mi><mrow><mi mathvariant="bold-italic">n</mi><mo>,</mo><mi mathvariant="bold-italic">m</mi></mrow><mi mathvariant="bold-italic">r</mi></msubsup><mrow><mfenced open="(" close=")"><mi mathvariant="bold-italic">σ</mi></mfenced></mrow></mrow></semantics></math></inline-formula> and Their Applications
In this paper, inspired by recent works, we define <i>q</i>-analogs of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mrow><mi>n</mi><mo...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/19/4159 |
| _version_ | 1797575555463249920 |
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| author | Hao Guan Sibel Koparal Neşe Ömür Waseem Ahmad Khan |
| author_facet | Hao Guan Sibel Koparal Neşe Ömür Waseem Ahmad Khan |
| author_sort | Hao Guan |
| collection | DOAJ |
| description | In this paper, inspired by recent works, we define <i>q</i>-analogs of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mrow><mi>n</mi><mo>,</mo><mi>m</mi></mrow></msub><mfenced open="(" close=")"><mi>σ</mi></mfenced></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>H</mi><mrow><mi>n</mi><mo>,</mo><mi>m</mi></mrow><mi>r</mi></msubsup><mfenced open="(" close=")"><mi>σ</mi></mfenced><mo>.</mo></mrow></semantics></math></inline-formula> By implementing them, we obtain new interesting results by taking the derivative or using generating functions. |
| first_indexed | 2024-03-10T21:40:12Z |
| format | Article |
| id | doaj.art-d0bb3eb07b2649339935e8a91428d8de |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T21:40:12Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d0bb3eb07b2649339935e8a91428d8de2023-11-19T14:44:09ZengMDPI AGMathematics2227-73902023-10-011119415910.3390/math11194159<i>q</i>-Analogs of <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold-italic">H</mi><mrow><mi mathvariant="bold-italic">n</mi><mo>,</mo><mi mathvariant="bold-italic">m</mi></mrow><mi mathvariant="bold-italic">r</mi></msubsup><mrow><mfenced open="(" close=")"><mi mathvariant="bold-italic">σ</mi></mfenced></mrow></mrow></semantics></math></inline-formula> and Their ApplicationsHao Guan0Sibel Koparal1Neşe Ömür2Waseem Ahmad Khan3Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, ChinaDepartment of Mathematics, Bursa Uludağ University, Bursa 16059, TurkeyDepartment of Mathematics, Kocaeli University, Kocaeli 41380, TurkeyDepartment of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi ArabiaIn this paper, inspired by recent works, we define <i>q</i>-analogs of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mrow><mi>n</mi><mo>,</mo><mi>m</mi></mrow></msub><mfenced open="(" close=")"><mi>σ</mi></mfenced></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>H</mi><mrow><mi>n</mi><mo>,</mo><mi>m</mi></mrow><mi>r</mi></msubsup><mfenced open="(" close=")"><mi>σ</mi></mfenced><mo>.</mo></mrow></semantics></math></inline-formula> By implementing them, we obtain new interesting results by taking the derivative or using generating functions.https://www.mdpi.com/2227-7390/11/19/4159alternative <i>q</i>-harmonic numbers<i>q</i>-polylogarithmsgeneralized <i>q</i>-hyperharmonic numbers of order <i>r</i> |
| spellingShingle | Hao Guan Sibel Koparal Neşe Ömür Waseem Ahmad Khan <i>q</i>-Analogs of <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold-italic">H</mi><mrow><mi mathvariant="bold-italic">n</mi><mo>,</mo><mi mathvariant="bold-italic">m</mi></mrow><mi mathvariant="bold-italic">r</mi></msubsup><mrow><mfenced open="(" close=")"><mi mathvariant="bold-italic">σ</mi></mfenced></mrow></mrow></semantics></math></inline-formula> and Their Applications Mathematics alternative <i>q</i>-harmonic numbers <i>q</i>-polylogarithms generalized <i>q</i>-hyperharmonic numbers of order <i>r</i> |
| title | <i>q</i>-Analogs of <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold-italic">H</mi><mrow><mi mathvariant="bold-italic">n</mi><mo>,</mo><mi mathvariant="bold-italic">m</mi></mrow><mi mathvariant="bold-italic">r</mi></msubsup><mrow><mfenced open="(" close=")"><mi mathvariant="bold-italic">σ</mi></mfenced></mrow></mrow></semantics></math></inline-formula> and Their Applications |
| title_full | <i>q</i>-Analogs of <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold-italic">H</mi><mrow><mi mathvariant="bold-italic">n</mi><mo>,</mo><mi mathvariant="bold-italic">m</mi></mrow><mi mathvariant="bold-italic">r</mi></msubsup><mrow><mfenced open="(" close=")"><mi mathvariant="bold-italic">σ</mi></mfenced></mrow></mrow></semantics></math></inline-formula> and Their Applications |
| title_fullStr | <i>q</i>-Analogs of <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold-italic">H</mi><mrow><mi mathvariant="bold-italic">n</mi><mo>,</mo><mi mathvariant="bold-italic">m</mi></mrow><mi mathvariant="bold-italic">r</mi></msubsup><mrow><mfenced open="(" close=")"><mi mathvariant="bold-italic">σ</mi></mfenced></mrow></mrow></semantics></math></inline-formula> and Their Applications |
| title_full_unstemmed | <i>q</i>-Analogs of <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold-italic">H</mi><mrow><mi mathvariant="bold-italic">n</mi><mo>,</mo><mi mathvariant="bold-italic">m</mi></mrow><mi mathvariant="bold-italic">r</mi></msubsup><mrow><mfenced open="(" close=")"><mi mathvariant="bold-italic">σ</mi></mfenced></mrow></mrow></semantics></math></inline-formula> and Their Applications |
| title_short | <i>q</i>-Analogs of <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold-italic">H</mi><mrow><mi mathvariant="bold-italic">n</mi><mo>,</mo><mi mathvariant="bold-italic">m</mi></mrow><mi mathvariant="bold-italic">r</mi></msubsup><mrow><mfenced open="(" close=")"><mi mathvariant="bold-italic">σ</mi></mfenced></mrow></mrow></semantics></math></inline-formula> and Their Applications |
| title_sort | i q i analogs of inline formula math display inline semantics mrow msubsup mi mathvariant bold italic h mi mrow mi mathvariant bold italic n mi mo mo mi mathvariant bold italic m mi mrow mi mathvariant bold italic r mi msubsup mrow mfenced open close mi mathvariant bold italic σ mi mfenced mrow mrow semantics math inline formula and their applications |
| topic | alternative <i>q</i>-harmonic numbers <i>q</i>-polylogarithms generalized <i>q</i>-hyperharmonic numbers of order <i>r</i> |
| url | https://www.mdpi.com/2227-7390/11/19/4159 |
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