Polynomials: Special Polynomials and Number-Theoretical Applications
Polynomials play a crucial role in many areas of mathematics including algebra, analysis, number theory, and probability theory. They also appear in physics, chemistry, and economics. Especially extensively studied are certain infinite families of polynomials. Here, we only mention some examples: Be...
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| Format: | Online |
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| Język: | angielski |
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MDPI - Multidisciplinary Digital Publishing Institute
2022
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| Dostęp online: | ONIX_20220111_9783036508184_252 |
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| collection | Directory of Open Access Books |
| description | Polynomials play a crucial role in many areas of mathematics including algebra, analysis, number theory, and probability theory. They also appear in physics, chemistry, and economics. Especially extensively studied are certain infinite families of polynomials. Here, we only mention some examples: Bernoulli, Euler, Gegenbauer, trigonometric, and orthogonal polynomials and their generalizations. There are several approaches to these classical mathematical objects. This Special Issue presents nine high quality research papers by leading researchers in this field. I hope the reading of this work will be useful for the new generation of mathematicians and for experienced researchers as well |
| format | Online |
| id | doab-20.500.12854ir-76516 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-765162024-03-28T03:32:32Z Polynomials: Special Polynomials and Number-Theoretical Applications Pintér, Ákos Shivley’s matrix polynomials Generating matrix functions Matrix recurrence relations summation formula Operational representations Euler polynomials higher degree equations degenerate Euler numbers and polynomials degenerate q-Euler numbers and polynomials degenerate Carlitz-type (p, q)-Euler numbers and polynomials 2D q-Appell polynomials twice-iterated 2D q-Appell polynomials determinant expressions recurrence relations 2D q-Bernoulli polynomials 2D q-Euler polynomials 2D q-Genocchi polynomials Apostol type Bernoulli Euler and Genocchi polynomials Euler numbers and polynomials Carlitz-type degenerate (p,q)-Euler numbers and polynomials Carlitz-type higher-order degenerate (p,q)-Euler numbers and polynomials symmetric identities (p, q)-cosine Bernoulli polynomials (p, q)-sine Bernoulli polynomials (p, q)-numbers (p, q)-trigonometric functions Bernstein operators rate of approximation Voronovskaja type asymptotic formula q-cosine Euler polynomials q-sine Euler polynomials q-trigonometric function q-exponential function multiquadric radial basis function radial polynomials the shape parameter meshless Kansa method thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science Polynomials play a crucial role in many areas of mathematics including algebra, analysis, number theory, and probability theory. They also appear in physics, chemistry, and economics. Especially extensively studied are certain infinite families of polynomials. Here, we only mention some examples: Bernoulli, Euler, Gegenbauer, trigonometric, and orthogonal polynomials and their generalizations. There are several approaches to these classical mathematical objects. This Special Issue presents nine high quality research papers by leading researchers in this field. I hope the reading of this work will be useful for the new generation of mathematicians and for experienced researchers as well 2022-01-11T13:34:18Z 2022-01-11T13:34:18Z 2021 book ONIX_20220111_9783036508184_252 9783036508184 9783036508191 https://directory.doabooks.org/handle/20.500.12854/76516 eng image/jpeg Attribution 4.0 International https://mdpi.com/books/pdfview/book/3962 https://mdpi.com/books/pdfview/book/3962 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-0365-0819-1 10.3390/books978-3-0365-0819-1 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783036508184 9783036508191 154 Basel, Switzerland open access |
| spellingShingle | Shivley’s matrix polynomials Generating matrix functions Matrix recurrence relations summation formula Operational representations Euler polynomials higher degree equations degenerate Euler numbers and polynomials degenerate q-Euler numbers and polynomials degenerate Carlitz-type (p, q)-Euler numbers and polynomials 2D q-Appell polynomials twice-iterated 2D q-Appell polynomials determinant expressions recurrence relations 2D q-Bernoulli polynomials 2D q-Euler polynomials 2D q-Genocchi polynomials Apostol type Bernoulli Euler and Genocchi polynomials Euler numbers and polynomials Carlitz-type degenerate (p,q)-Euler numbers and polynomials Carlitz-type higher-order degenerate (p,q)-Euler numbers and polynomials symmetric identities (p, q)-cosine Bernoulli polynomials (p, q)-sine Bernoulli polynomials (p, q)-numbers (p, q)-trigonometric functions Bernstein operators rate of approximation Voronovskaja type asymptotic formula q-cosine Euler polynomials q-sine Euler polynomials q-trigonometric function q-exponential function multiquadric radial basis function radial polynomials the shape parameter meshless Kansa method thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science Polynomials: Special Polynomials and Number-Theoretical Applications |
| title | Polynomials: Special Polynomials and Number-Theoretical Applications |
| title_full | Polynomials: Special Polynomials and Number-Theoretical Applications |
| title_fullStr | Polynomials: Special Polynomials and Number-Theoretical Applications |
| title_full_unstemmed | Polynomials: Special Polynomials and Number-Theoretical Applications |
| title_short | Polynomials: Special Polynomials and Number-Theoretical Applications |
| title_sort | polynomials special polynomials and number theoretical applications |
| topic | Shivley’s matrix polynomials Generating matrix functions Matrix recurrence relations summation formula Operational representations Euler polynomials higher degree equations degenerate Euler numbers and polynomials degenerate q-Euler numbers and polynomials degenerate Carlitz-type (p, q)-Euler numbers and polynomials 2D q-Appell polynomials twice-iterated 2D q-Appell polynomials determinant expressions recurrence relations 2D q-Bernoulli polynomials 2D q-Euler polynomials 2D q-Genocchi polynomials Apostol type Bernoulli Euler and Genocchi polynomials Euler numbers and polynomials Carlitz-type degenerate (p,q)-Euler numbers and polynomials Carlitz-type higher-order degenerate (p,q)-Euler numbers and polynomials symmetric identities (p, q)-cosine Bernoulli polynomials (p, q)-sine Bernoulli polynomials (p, q)-numbers (p, q)-trigonometric functions Bernstein operators rate of approximation Voronovskaja type asymptotic formula q-cosine Euler polynomials q-sine Euler polynomials q-trigonometric function q-exponential function multiquadric radial basis function radial polynomials the shape parameter meshless Kansa method thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science |
| topic_facet | Shivley’s matrix polynomials Generating matrix functions Matrix recurrence relations summation formula Operational representations Euler polynomials higher degree equations degenerate Euler numbers and polynomials degenerate q-Euler numbers and polynomials degenerate Carlitz-type (p, q)-Euler numbers and polynomials 2D q-Appell polynomials twice-iterated 2D q-Appell polynomials determinant expressions recurrence relations 2D q-Bernoulli polynomials 2D q-Euler polynomials 2D q-Genocchi polynomials Apostol type Bernoulli Euler and Genocchi polynomials Euler numbers and polynomials Carlitz-type degenerate (p,q)-Euler numbers and polynomials Carlitz-type higher-order degenerate (p,q)-Euler numbers and polynomials symmetric identities (p, q)-cosine Bernoulli polynomials (p, q)-sine Bernoulli polynomials (p, q)-numbers (p, q)-trigonometric functions Bernstein operators rate of approximation Voronovskaja type asymptotic formula q-cosine Euler polynomials q-sine Euler polynomials q-trigonometric function q-exponential function multiquadric radial basis function radial polynomials the shape parameter meshless Kansa method thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general thema EDItEUR::P Mathematics and Science |
| url | ONIX_20220111_9783036508184_252 |