On the (<i>p</i>, <i>q</i>)–Chebyshev Polynomials and Related Polynomials
In this paper, we introduce <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-form...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/2/136 |
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| author | Can Kızılateş Naim Tuğlu Bayram Çekim |
| author_facet | Can Kızılateş Naim Tuğlu Bayram Çekim |
| author_sort | Can Kızılateş |
| collection | DOAJ |
| description | In this paper, we introduce <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>⁻Chebyshev polynomials of the first and second kind that reduces the <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>⁻Fibonacci and the <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>⁻Lucas polynomials. These polynomials have explicit forms and generating functions are given. Then, derivative properties between these first and second kind polynomials, determinant representations, multilateral and multilinear generating functions are derived. |
| first_indexed | 2024-12-13T02:42:48Z |
| format | Article |
| id | doaj.art-3ceaf244e5ac42ac8bb47c75d2d192fa |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-13T02:42:48Z |
| publishDate | 2019-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3ceaf244e5ac42ac8bb47c75d2d192fa2022-12-22T00:02:15ZengMDPI AGMathematics2227-73902019-02-017213610.3390/math7020136math7020136On the (<i>p</i>, <i>q</i>)–Chebyshev Polynomials and Related PolynomialsCan Kızılateş0Naim Tuğlu1Bayram Çekim2Faculty of Art and Science, Department of Mathematics, Zonguldak Bülent Ecevit University, Zonguldak 67100, TurkeyFaculty of Science, Department of Mathematics, Gazi University, Teknikokullar, Ankara 06500, TurkeyFaculty of Science, Department of Mathematics, Gazi University, Teknikokullar, Ankara 06500, TurkeyIn this paper, we introduce <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>⁻Chebyshev polynomials of the first and second kind that reduces the <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>⁻Fibonacci and the <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>⁻Lucas polynomials. These polynomials have explicit forms and generating functions are given. Then, derivative properties between these first and second kind polynomials, determinant representations, multilateral and multilinear generating functions are derived.https://www.mdpi.com/2227-7390/7/2/136(<i>p</i>, <i>q</i>)–Chebyshev polynomials(<i>p</i>, <i>q</i>)–Fibonacci polynomialsmultilateral generating functionsmultilinear generating functions. |
| spellingShingle | Can Kızılateş Naim Tuğlu Bayram Çekim On the (<i>p</i>, <i>q</i>)–Chebyshev Polynomials and Related Polynomials Mathematics (<i>p</i>, <i>q</i>)–Chebyshev polynomials (<i>p</i>, <i>q</i>)–Fibonacci polynomials multilateral generating functions multilinear generating functions. |
| title | On the (<i>p</i>, <i>q</i>)–Chebyshev Polynomials and Related Polynomials |
| title_full | On the (<i>p</i>, <i>q</i>)–Chebyshev Polynomials and Related Polynomials |
| title_fullStr | On the (<i>p</i>, <i>q</i>)–Chebyshev Polynomials and Related Polynomials |
| title_full_unstemmed | On the (<i>p</i>, <i>q</i>)–Chebyshev Polynomials and Related Polynomials |
| title_short | On the (<i>p</i>, <i>q</i>)–Chebyshev Polynomials and Related Polynomials |
| title_sort | on the i p i i q i chebyshev polynomials and related polynomials |
| topic | (<i>p</i>, <i>q</i>)–Chebyshev polynomials (<i>p</i>, <i>q</i>)–Fibonacci polynomials multilateral generating functions multilinear generating functions. |
| url | https://www.mdpi.com/2227-7390/7/2/136 |
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