Year: 2025
Type: article
Abstract: Simple asymptotic expansions for the Jacobi functions P ν ( α , β ) ( z ) P_\nu ^{(\alpha , \beta )}(z) and Q ν ( α , β ) ( z ) Q_\nu ^{(\alpha , \beta )}(z) for large degree ν \nu , with fixed parameters α \alpha and β \beta , are surprisingly rare in the literature, with only a few special cases covered. This paper addresses this notable gap by deriving simple (inverse) factorial expansions for these functions, complemented by explicit and computable error bounds. Additionally, we provide analogous results for the associated functions Q ν ( α , β ) ( x ) \mathrm {Q}_\nu ^{(\alpha , \beta )}(x) and Q ν ( α , β ) ( x ) \mathsf {Q}_\nu ^{(\alpha , \beta )}(x) .
Source: Mathematics of Computation
DOI: 10.1090/mcom/4145
Author: Gergő Nemes
Institution: Harbin Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415672850