The Asymptotic Expansions of Hankel Transforms and Related Integrals

Asymptotic Expansions for Integrals

Asymptotic Expansions of Symmetric Standard Elliptic Integrals

Symmetric standard elliptic integrals are considered when one of their parameters is larger than the others. Distributional approach is used for deriving five convergent expansions of these integrals in inverse powers of the respective five possible asymptotic parameters. Four of these expansions involve also a logarithmic term in the asymptotic variable. Coefficients of these expansions are ob...

the evaluation of language related engagment and task related engagment with the purpose of investigating the effect of metatalk and task typology

abstract while task-based instruction is considered as the most effective way to learn a language in the related literature, it is oversimplified on various grounds. different variables may affect how students are engaged with not only the language but also with the task itself. the present study was conducted to investigate language and task related engagement on the basis of the task typolog...

Laplace Asymptotic Expansions for Gaussian Functional Integrals

We obtain a Laplace asymptotic expansion, in orders of λ, of Eρx { G(λx)e −2F (λx)} } the expectation being with respect to a Gaussian process. We extend a result of Pincus [9] and build upon the previous work of Davies and Truman [1, 2, 3, 4]. Our methods differ from those of Ellis and Rosen [6, 7, 8] in that we use the supremum norm to simplify the application of the result. A.M.S. Classifica...

A Note on Asymptotic Evaluation of Some Hankel Transforms

Asymptotic behavior of the integral '((w) = r e-"%(wx)f(x2)xdx is investigated, where J0(x) is the Bessel function of the first kind and w is a large positive parameter. It is shown that IAw) decays exponentially like e~y"' , y > 0, when/(z) is an entire function subject to a suitable growth condition. A complete asymptotic expansion is obtained when /( z ) is a meromorphic function satisfying ...