An affirmative answer to an open problem on Ramanujan's asymptotic formula of zero-balanced hypergeometric function
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915231429558272 |
|---|---|
| author | Wang, Miao-kun Yang, Zhen-hang Zhao, Tie-hong |
| author_facet | Wang, Miao-kun Yang, Zhen-hang Zhao, Tie-hong |
| contents | In this paper, by using recurrence method and new properties of beta function and Ramanujan $R$-function, we prove the absolute monotonicity result for a function related to Ramanujan asymptotic formula of zero-balanced hypergeometric function, which gives an affirmative answer to an open problem proposed by Anderson Vamanamurthy and Vuorinen \cite{Anderson-CIIQM-JW-1997} in 1997. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04521 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An affirmative answer to an open problem on Ramanujan's asymptotic formula of zero-balanced hypergeometric function Wang, Miao-kun Yang, Zhen-hang Zhao, Tie-hong Classical Analysis and ODEs 33C05, 26A48, 40A05, 41A10 In this paper, by using recurrence method and new properties of beta function and Ramanujan $R$-function, we prove the absolute monotonicity result for a function related to Ramanujan asymptotic formula of zero-balanced hypergeometric function, which gives an affirmative answer to an open problem proposed by Anderson Vamanamurthy and Vuorinen \cite{Anderson-CIIQM-JW-1997} in 1997. |
| title | An affirmative answer to an open problem on Ramanujan's asymptotic formula of zero-balanced hypergeometric function |
| topic | Classical Analysis and ODEs 33C05, 26A48, 40A05, 41A10 |
| url | https://arxiv.org/abs/2504.04521 |