The Generating Functions for Special Pringsheim Continued Fractions
In previous works, some relations between Pringsheim continued fractions and vertices of the paths of minimal length on the suborbital graphs $\mathrm{\mathbf{F}}_{u,N}$ were investigated. Then, for special vertices, the relations between these vertices and Fibonacci numbers were examined. On the ot...
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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2020-06-01
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| Series: | Communications in Advanced Mathematical Sciences |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/1177806 |
| _version_ | 1827340841465675776 |
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| author | Ali Hikmet Değer Ümmügülsün Akbaba |
| author_facet | Ali Hikmet Değer Ümmügülsün Akbaba |
| author_sort | Ali Hikmet Değer |
| collection | DOAJ |
| description | In previous works, some relations between Pringsheim continued fractions and vertices of the paths of minimal length on the suborbital graphs $\mathrm{\mathbf{F}}_{u,N}$ were investigated. Then, for special vertices, the relations between these vertices and Fibonacci numbers were examined. On the other hand, Koshy studied relation between recurrence relations of Fibonacci numbers, Pell numbers and generating functions. In this work, it is showed that every vertex on the path of minimal length of suborbital graph $\mathrm{\mathbf{F}}_{u,N}$ has a Pringsheim continued fraction. Then, by Koshy's motivation, the generating function of the recurrence relation of these pringsheim continued fractions are examined. |
| first_indexed | 2024-03-07T21:27:19Z |
| format | Article |
| id | doaj.art-e418011df2b649f8afa27e2b38039823 |
| institution | Directory Open Access Journal |
| issn | 2651-4001 |
| language | English |
| last_indexed | 2024-03-07T21:27:19Z |
| publishDate | 2020-06-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Communications in Advanced Mathematical Sciences |
| spelling | doaj.art-e418011df2b649f8afa27e2b380398232024-02-27T04:36:36ZengEmrah Evren KARACommunications in Advanced Mathematical Sciences2651-40012020-06-0132748110.33434/cams.6906431225The Generating Functions for Special Pringsheim Continued FractionsAli Hikmet Değer0Ümmügülsün Akbaba1Karadeniz Technical UniversityKaradeniz Technical UniversityIn previous works, some relations between Pringsheim continued fractions and vertices of the paths of minimal length on the suborbital graphs $\mathrm{\mathbf{F}}_{u,N}$ were investigated. Then, for special vertices, the relations between these vertices and Fibonacci numbers were examined. On the other hand, Koshy studied relation between recurrence relations of Fibonacci numbers, Pell numbers and generating functions. In this work, it is showed that every vertex on the path of minimal length of suborbital graph $\mathrm{\mathbf{F}}_{u,N}$ has a Pringsheim continued fraction. Then, by Koshy's motivation, the generating function of the recurrence relation of these pringsheim continued fractions are examined.https://dergipark.org.tr/tr/download/article-file/1177806fibonacci sequence generating functionspell sequencecontinued fractionssuborbital graphs |
| spellingShingle | Ali Hikmet Değer Ümmügülsün Akbaba The Generating Functions for Special Pringsheim Continued Fractions Communications in Advanced Mathematical Sciences fibonacci sequence generating functions pell sequence continued fractions suborbital graphs |
| title | The Generating Functions for Special Pringsheim Continued Fractions |
| title_full | The Generating Functions for Special Pringsheim Continued Fractions |
| title_fullStr | The Generating Functions for Special Pringsheim Continued Fractions |
| title_full_unstemmed | The Generating Functions for Special Pringsheim Continued Fractions |
| title_short | The Generating Functions for Special Pringsheim Continued Fractions |
| title_sort | generating functions for special pringsheim continued fractions |
| topic | fibonacci sequence generating functions pell sequence continued fractions suborbital graphs |
| url | https://dergipark.org.tr/tr/download/article-file/1177806 |
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