Hypergeometric-Type Sequences
Abstrak
We introduce hypergeometric-type sequences. They are linear combinations of interlaced hypergeometric sequences (of arbitrary interlacements). We prove that they form a subring of the ring of holonomic sequences. An interesting family of sequences in this class are those defined by trigonometric functions with linear arguments in the index and $π$, such as Chebyshev polynomials, $\left(\sin^2\left(n\,π/4\right)\cdot\cos\left(n\,π/6\right)\right)_n$, and compositions like $\left(\sin\left(\cos(nπ/3)π\right)\right)_n$. We describe an algorithm that computes a hypergeometric-type normal form of a given holonomic $n\text{th}$ term whenever it exists. Our implementation enables us to generate several identities for terms defined via trigonometric functions.
Penulis (1)
Bertrand Teguia Tabuguia
Akses Cepat
- Tahun Terbit
- 2023
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓