Power-series unification and reversion
Applied Mathematics and Computation
SIAM Journal on Mathematical Analysis
GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable
ACM Transactions on Mathematical Software (TOMS)
Fast computation of some asymptotic functional inverses
Journal of Symbolic Computation
Symbolic asymptotics: multiseries of inverse functions
Journal of Symbolic Computation
Fast Algorithms for Manipulating Formal Power Series
Journal of the ACM (JACM)
Solution of transcendental equations by series reversion
Communications of the ACM
Communications of the ACM
Evaluation of the modified Bessel function of the third kind of imaginary orders
Journal of Computational Physics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
On the coefficients that arise from Laplace's method
Journal of Computational and Applied Mathematics
Hi-index | 7.30 |
We examine a Maple implementation of two distinct approaches to Laplace's method used to obtain asymptotic expansions of Laplace-type integrals. One algorithm uses power series reversion, whereas the other expands all quantities in Taylor or Puiseux series. These algorithms are used to derive asymptotic expansions for the real valued modified Bessel functions of pure imaginary order and real argument that mimic the well-known corresponding expansions for the unmodified Bessel functions.