Sharp estimates for Hübner’s upper bound function with applications

Autor:	Song-liang Qiu, Liang-Yu Ren
Rok vydání:	2010
Předmět:	Distortion function symbols.namesake Pure mathematics Modular equation Schwarz lemma Applied Mathematics Mathematical analysis symbols Elementary function Function (mathematics) Upper and lower bounds Mathematics Ramanujan's sum
Zdroj:	Applied Mathematics-A Journal of Chinese Universities. 25:227-235
ISSN:	1993-0445 1005-1031
DOI:	10.1007/s11766-010-2203-3
Popis:	New better estimates, which are given in terms of elementary functions, for the function r 7→ (2/�)(1 − r 2 )K(r)K ' (r) + log r appearing in Hubner's sharp upper bound for the Hersch-Pfluger distortion function are obtained. With these estimates, some known bounds for the Hersch-Pfluger distortion function in quasiconformal theory are improved, thus improving the explicit quasiconformal Schwarz lemma and some known estimates for the solutions to the Ramanujan modular equations.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::615f46c876d9a4fb519500d19ca8b834 https://doi.org/10.1007/s11766-010-2203-3 Zobrazit plný text záznamu Full text from SpringerLink