Miscellaneous summation, integration, and transformation formulas
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913685504524288 |
|---|---|
| author | Nicholson, Martin |
| author_facet | Nicholson, Martin |
| contents | This is a discussion of miscellaneous summation, integration and transformation formulas obtained using Fourier analysis. The topics covered are: Series of the form $\sum_{n\in\mathbb{Z}} c_ne^{πi γn^2}$; Fusion of integrals, and in particular fusion of $q$-beta integrals related to Gauss-Fourier transform, and a related family of eigenfunctions of the cosine Fourier transform; Summation formulas of the type $\sum_{n\ge 1}\frac{χ(n)}{n}\,φ(n)$ with Dirichlet characters; Trigonometric Fourier series expansion of hypergeometric functions of the argument $\sin^2x$; Modifications of the inverse tangent integral and identities for corresponding infinite products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10805 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Miscellaneous summation, integration, and transformation formulas Nicholson, Martin Classical Analysis and ODEs 42A99 (Primary) 42A16, 42A38 (Secondary) This is a discussion of miscellaneous summation, integration and transformation formulas obtained using Fourier analysis. The topics covered are: Series of the form $\sum_{n\in\mathbb{Z}} c_ne^{πi γn^2}$; Fusion of integrals, and in particular fusion of $q$-beta integrals related to Gauss-Fourier transform, and a related family of eigenfunctions of the cosine Fourier transform; Summation formulas of the type $\sum_{n\ge 1}\frac{χ(n)}{n}\,φ(n)$ with Dirichlet characters; Trigonometric Fourier series expansion of hypergeometric functions of the argument $\sin^2x$; Modifications of the inverse tangent integral and identities for corresponding infinite products. |
| title | Miscellaneous summation, integration, and transformation formulas |
| topic | Classical Analysis and ODEs 42A99 (Primary) 42A16, 42A38 (Secondary) |
| url | https://arxiv.org/abs/2404.10805 |