In this study, the numerical solutions have been obtained by using the asymptotic expansions
They cover asymptotic expansions
and series, asymptotic methods for solving nonlinear equations, the perturbation of nonlinear oscillations, a nonlinear oscillator in a potential well, auto-resonances in nonlinear systems, asymptotics for loss of stability, and systems of coupled oscillators.
In particular, we will study existence, multiplicity and asymptotic expansions
of solutions when the competition parameter tends to infinity.
epsilon],[delta]](*) by constructing asymptotic expansions
of its probability densities, which are associated with the adjoint operator [L.
In a similar way, the asymptotic expansions
by allowing further terms in the asymptotic expansions
with exponents between [alpha] and [alpha] + 1, with additional assumptions on the coefficients.
Using asymptotic expansions
, Efron (1975) demonstrated that LLD can be less efficient than LDA when the assumptions of LDA are satisfied.
Olde Daalhuis, Asymptotic expansions
of q-gamma, q-exponential and q-bessel functions, Journal of Mathematical Analysis and Applications, 186 (1994), 896-913.
The main purpose of this paper is to obtain the first term in the asymptotic expansions
and analytic continuations of the H-function have been discussed by Braaksma ((1)).
In the context of computing asymptotic expansions
of sums and series, usually the most useful form of the Euler-Maclaurin formula is
4), we use the ideas from [6,10] of asymptotic expansions
of the Bessel functions.