| Περίληψη: |
Simple asymptotic expansions for the Jacobi functions P_\nu ^{(\alpha, \beta)}(z) and Q_\nu ^{(\alpha, \beta)}(z) for large degree \nu, with fixed parameters \alpha and \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 \mathrm {Q}_\nu ^{(\alpha, \beta)}(x) and \mathsf {Q}_\nu ^{(\alpha, \beta)}(x). [ABSTRACT FROM AUTHOR] |
