Rotationally Symmetric Lacunary Functions and Products of Centered Polygonal Lacunary Functions
This work builds upon previous studies of centered polygonal lacunary functions by presenting proofs of theorems showing how rotational and dihedral mirror symmetry manifest in these lacunary functions at the modulus level. These theorems then provide a general framework for constructing other lacun...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-05-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/4/2/24 |
| _version_ | 1797566933540798464 |
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| author | L. K. Mork Keith Sullivan Trenton Vogt Darin J. Ulness |
| author_facet | L. K. Mork Keith Sullivan Trenton Vogt Darin J. Ulness |
| author_sort | L. K. Mork |
| collection | DOAJ |
| description | This work builds upon previous studies of centered polygonal lacunary functions by presenting proofs of theorems showing how rotational and dihedral mirror symmetry manifest in these lacunary functions at the modulus level. These theorems then provide a general framework for constructing other lacunary functions that exhibit the same symmetries. These investigations enable one to better explore the effects of the gap behavior on the qualitative features of the associated lacunary functions. Further, two renormalized products of centered polygonal lacunary functions are defined and a connection to Ramanunjan’s triangular lacunary series is made via several theorems. |
| first_indexed | 2024-03-10T19:34:26Z |
| format | Article |
| id | doaj.art-2e673d9ff0714a14a23537ad6708a0d6 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T19:34:26Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-2e673d9ff0714a14a23537ad6708a0d62023-11-20T01:49:58ZengMDPI AGFractal and Fractional2504-31102020-05-01422410.3390/fractalfract4020024Rotationally Symmetric Lacunary Functions and Products of Centered Polygonal Lacunary FunctionsL. K. Mork0Keith Sullivan1Trenton Vogt2Darin J. Ulness3Department of Mathematics, Concordia College, Moorhead, MN 56562, USADepartment of Mathematics, Concordia College, Moorhead, MN 56562, USADepartment of Chemistry, Concordia College, Moorhead, MN 56562, USADepartment of Chemistry, Concordia College, Moorhead, MN 56562, USAThis work builds upon previous studies of centered polygonal lacunary functions by presenting proofs of theorems showing how rotational and dihedral mirror symmetry manifest in these lacunary functions at the modulus level. These theorems then provide a general framework for constructing other lacunary functions that exhibit the same symmetries. These investigations enable one to better explore the effects of the gap behavior on the qualitative features of the associated lacunary functions. Further, two renormalized products of centered polygonal lacunary functions are defined and a connection to Ramanunjan’s triangular lacunary series is made via several theorems.https://www.mdpi.com/2504-3110/4/2/24lacunary functiongap functioncentered polygonal numbersnatural boundarysingularitiesrenormalization |
| spellingShingle | L. K. Mork Keith Sullivan Trenton Vogt Darin J. Ulness Rotationally Symmetric Lacunary Functions and Products of Centered Polygonal Lacunary Functions Fractal and Fractional lacunary function gap function centered polygonal numbers natural boundary singularities renormalization |
| title | Rotationally Symmetric Lacunary Functions and Products of Centered Polygonal Lacunary Functions |
| title_full | Rotationally Symmetric Lacunary Functions and Products of Centered Polygonal Lacunary Functions |
| title_fullStr | Rotationally Symmetric Lacunary Functions and Products of Centered Polygonal Lacunary Functions |
| title_full_unstemmed | Rotationally Symmetric Lacunary Functions and Products of Centered Polygonal Lacunary Functions |
| title_short | Rotationally Symmetric Lacunary Functions and Products of Centered Polygonal Lacunary Functions |
| title_sort | rotationally symmetric lacunary functions and products of centered polygonal lacunary functions |
| topic | lacunary function gap function centered polygonal numbers natural boundary singularities renormalization |
| url | https://www.mdpi.com/2504-3110/4/2/24 |
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