Watson’s lemma and Laplace’s method provide asymptotic expansions of Laplace integrals F(z)≔∫0∞e−zf(t)g(t)dt for large values the parameter z. They are useful tools in approximation special functions that have a integral representation. But most important examples functions, expansion derived by means or is not convergent. A modification was introduced [Nielsen, 1906] where, use inverse factori...

In this paper we apply the Homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of Sturm-liouville type on $[0,pi]$ with Neumann conditions $(y'(0)=y'(pi)=0)$ where $q$ is a real-valued Sign-indefinite number of $C^{1}[0,pi]$ and $lambda$ is a real parameter.

In this paper, we study dynamic commensalism model with nonmonotic functional response, density dependent birth rates on time scales and derive sufficient conditions for the permanence. We also establish the existence and uniform asymptotic stability of unique almost periodic positive solution of the model by using Lyapunov functional method.

In this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

This paper considers an Extended Generalized Half Logistic distribution. We derive some properties of this distribution and then we discuss estimation of the distribution parameters by the methods of moments, maximum likelihood and the new method of minimum spacing distance estimator based on complete data. Also, maximum likelihood equations for estimating the parameters based on Type-I and Typ...

In this paper we discuss on the fixed points of asymptotic contractions and Boyd-Wong type contractions in uniform spaces equipped with an E-distance. A new version ofKirk's fixed point theorem is given for asymptotic contractions and Boyd-Wong type contractions is investigated in uniform spaces.

Published 15 We obtain a new proof of an asymptotic formula for the coefficients of the j-invariant 16 of elliptic curves. Our proof does not use the circle method. We use Laplace's method 17 of steepest descent and the Hardy–Ramanujan asymptotic formula for the partition 18 function. (The latter asymptotic formula can be derived without the circle method.)

We present a method for the numerical quadrature of highly oscillatory integrals with stationary points. We begin with the derivation of a new asymptotic expansion, which has the property that the accuracy improves as the frequency of oscillations increases. This asymptotic expansion is closely related to the method of stationary phase, but presented in a way that allows the derivation of an al...