Families of self-inverse functions and dilogarithm identities
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917063706017792 |
|---|---|
| author | Alha, Lauri |
| author_facet | Alha, Lauri |
| contents | We introduce a self-inverse function via an integral equivalent to a two-term combination of dilogarithms. We refer to this function as a fundamental form, since there is a family of extensions of this function that satisfy similar self-inverse and symmetric properties. We also construct a family of functions generalizing the fundamental form via two auxiliary parameters, which we refer to as shape and scale factors. Through new integration techniques, we introduce and prove a variety of dilogarithm identities and evaluations for dilogarithm ladders and for two-term dilogarithm combinations. The functions$ \gemini_{a}^{b}(x)$ we introduce are referred to as gemini functions and may be seen as providing a broad framework in the derivation of and application of dilogarithm identities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07598 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Families of self-inverse functions and dilogarithm identities Alha, Lauri Classical Analysis and ODEs We introduce a self-inverse function via an integral equivalent to a two-term combination of dilogarithms. We refer to this function as a fundamental form, since there is a family of extensions of this function that satisfy similar self-inverse and symmetric properties. We also construct a family of functions generalizing the fundamental form via two auxiliary parameters, which we refer to as shape and scale factors. Through new integration techniques, we introduce and prove a variety of dilogarithm identities and evaluations for dilogarithm ladders and for two-term dilogarithm combinations. The functions$ \gemini_{a}^{b}(x)$ we introduce are referred to as gemini functions and may be seen as providing a broad framework in the derivation of and application of dilogarithm identities. |
| title | Families of self-inverse functions and dilogarithm identities |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2509.07598 |