Academic Journal
Large-degree asymptotic expansions for the Jacobi and related functions.
| Τίτλος: | Large-degree asymptotic expansions for the Jacobi and related functions. |
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| Συγγραφείς: | Nemes, Gergő1 (AUTHOR) |
| Πηγή: | Mathematics of Computation. Jan2027, Vol. 96 Issue 363, p255-299. 45p. |
| Θεματικοί όροι: | *Asymptotic expansions, *Jacobi polynomials, *Mathematical analysis, *Special functions |
| 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] |
| Βάση Δεδομένων: | Academic Search Index |
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