Orthogonal Polynomials on Radial Rays in the Complex Plane: Construction, Properties and Applications
Orthogonal polynomials on radial rays in the complex plane were introduced and studied intensively in several papers almost three decades ago. This paper presents an account of such kinds of orthogonality in the complex plane, as well as a number of new results and examples. In addition to several t...
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2025-01-01
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| author | Gradimir V. Milovanović |
| author_facet | Gradimir V. Milovanović |
| author_sort | Gradimir V. Milovanović |
| collection | DOAJ |
| description | Orthogonal polynomials on radial rays in the complex plane were introduced and studied intensively in several papers almost three decades ago. This paper presents an account of such kinds of orthogonality in the complex plane, as well as a number of new results and examples. In addition to several types of standard orthogonality, the concept of orthogonality on arbitrary radial rays is introduced, some or all of which may be infinite. A general method for numerical constructing, the so-called <i>discretized Stieltjes–Gautschi procedure</i>, is described and several interesting examples are presented. The main properties, zero distribution and some applications are also given. Special attention is paid to completely symmetric cases. Recurrence relations for such kinds of orthogonal polynomials and their zero distribution, as well as a connection with the standard polynomials orthogonal on the real line, are derived, including the corresponding linear differential equation of the second order. Finally, some applications in physics and electrostatics are mentioned. |
| format | Article |
| id | doaj-art-c5f60e9123954975a0f4f1720836153a |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-c5f60e9123954975a0f4f1720836153a2025-01-24T13:22:18ZengMDPI AGAxioms2075-16802025-01-011416510.3390/axioms14010065Orthogonal Polynomials on Radial Rays in the Complex Plane: Construction, Properties and ApplicationsGradimir V. Milovanović0Serbian Academy of Sciences and Arts, 11000 Belgrade, SerbiaOrthogonal polynomials on radial rays in the complex plane were introduced and studied intensively in several papers almost three decades ago. This paper presents an account of such kinds of orthogonality in the complex plane, as well as a number of new results and examples. In addition to several types of standard orthogonality, the concept of orthogonality on arbitrary radial rays is introduced, some or all of which may be infinite. A general method for numerical constructing, the so-called <i>discretized Stieltjes–Gautschi procedure</i>, is described and several interesting examples are presented. The main properties, zero distribution and some applications are also given. Special attention is paid to completely symmetric cases. Recurrence relations for such kinds of orthogonal polynomials and their zero distribution, as well as a connection with the standard polynomials orthogonal on the real line, are derived, including the corresponding linear differential equation of the second order. Finally, some applications in physics and electrostatics are mentioned.https://www.mdpi.com/2075-1680/14/1/65orthogonal polynomialsradial raysinner productnormrecurrence relationzeros |
| spellingShingle | Gradimir V. Milovanović Orthogonal Polynomials on Radial Rays in the Complex Plane: Construction, Properties and Applications Axioms orthogonal polynomials radial rays inner product norm recurrence relation zeros |
| title | Orthogonal Polynomials on Radial Rays in the Complex Plane: Construction, Properties and Applications |
| title_full | Orthogonal Polynomials on Radial Rays in the Complex Plane: Construction, Properties and Applications |
| title_fullStr | Orthogonal Polynomials on Radial Rays in the Complex Plane: Construction, Properties and Applications |
| title_full_unstemmed | Orthogonal Polynomials on Radial Rays in the Complex Plane: Construction, Properties and Applications |
| title_short | Orthogonal Polynomials on Radial Rays in the Complex Plane: Construction, Properties and Applications |
| title_sort | orthogonal polynomials on radial rays in the complex plane construction properties and applications |
| topic | orthogonal polynomials radial rays inner product norm recurrence relation zeros |
| url | https://www.mdpi.com/2075-1680/14/1/65 |
| work_keys_str_mv | AT gradimirvmilovanovic orthogonalpolynomialsonradialraysinthecomplexplaneconstructionpropertiesandapplications |