New Summation and Integral Representations for 2-Variable (<i>p</i>,<i>q</i>)-Hermite Polynomials
In this paper, we introduce and study new features for 2-variable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/13/3/196 |
| _version_ | 1797242108631842816 |
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| author | Nusrat Raza Mohammed Fadel Wei-Shih Du |
| author_facet | Nusrat Raza Mohammed Fadel Wei-Shih Du |
| author_sort | Nusrat Raza |
| collection | DOAJ |
| description | In this paper, we introduce and study new features for 2-variable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Hermite polynomials, such as the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-diffusion equation, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-differential formula and integral representations. In addition, we establish some summation models and their <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-derivatives. Certain parting remarks and nontrivial examples are also provided. |
| first_indexed | 2024-04-24T18:33:59Z |
| format | Article |
| id | doaj.art-ff69707116bd42bab2194216c15c0a37 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-04-24T18:33:59Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-ff69707116bd42bab2194216c15c0a372024-03-27T13:21:05ZengMDPI AGAxioms2075-16802024-03-0113319610.3390/axioms13030196New Summation and Integral Representations for 2-Variable (<i>p</i>,<i>q</i>)-Hermite PolynomialsNusrat Raza0Mohammed Fadel1Wei-Shih Du2Mathematics Section, Women’s College, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Lahej University, Lahej 73560, YemenDepartment of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, TaiwanIn this paper, we introduce and study new features for 2-variable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Hermite polynomials, such as the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-diffusion equation, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-differential formula and integral representations. In addition, we establish some summation models and their <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-derivatives. Certain parting remarks and nontrivial examples are also provided.https://www.mdpi.com/2075-1680/13/3/196(<i>p</i>,<i>q</i>)-calculus2-variable (<i>p</i>,<i>q</i>)-Hermite polynomialsshift operator for polynomials(<i>p</i>,<i>q</i>)-differential equation summation formulasintegral representations |
| spellingShingle | Nusrat Raza Mohammed Fadel Wei-Shih Du New Summation and Integral Representations for 2-Variable (<i>p</i>,<i>q</i>)-Hermite Polynomials Axioms (<i>p</i>,<i>q</i>)-calculus 2-variable (<i>p</i>,<i>q</i>)-Hermite polynomials shift operator for polynomials (<i>p</i>,<i>q</i>)-differential equation summation formulas integral representations |
| title | New Summation and Integral Representations for 2-Variable (<i>p</i>,<i>q</i>)-Hermite Polynomials |
| title_full | New Summation and Integral Representations for 2-Variable (<i>p</i>,<i>q</i>)-Hermite Polynomials |
| title_fullStr | New Summation and Integral Representations for 2-Variable (<i>p</i>,<i>q</i>)-Hermite Polynomials |
| title_full_unstemmed | New Summation and Integral Representations for 2-Variable (<i>p</i>,<i>q</i>)-Hermite Polynomials |
| title_short | New Summation and Integral Representations for 2-Variable (<i>p</i>,<i>q</i>)-Hermite Polynomials |
| title_sort | new summation and integral representations for 2 variable i p i i q i hermite polynomials |
| topic | (<i>p</i>,<i>q</i>)-calculus 2-variable (<i>p</i>,<i>q</i>)-Hermite polynomials shift operator for polynomials (<i>p</i>,<i>q</i>)-differential equation summation formulas integral representations |
| url | https://www.mdpi.com/2075-1680/13/3/196 |
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