کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4642762 1632056 2007 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Asymptotic expansions of Mellin convolutions by means of analytic continuation
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Asymptotic expansions of Mellin convolutions by means of analytic continuation
چکیده انگلیسی

We present a method for deriving asymptotic expansions of integrals of the form ∫0∞f(t)h(xt)dt for small x based on analytic continuation. The expansion is given in terms of two asymptotic sequences, the coefficients of both sequences being Mellin transforms of h   and ff. Many known and unknown asymptotic expansions of important integral transforms are derived trivially from the approach presented here. This paper reconsiders earlier work of McClure and Wong [Explicit error terms for asymptotic expansions of Stieltjes transforms, J. Inst. Math. Appl. 22 (1978) 129–145; Exact remainders for asymptotic expansions of fractional integrals, J. Inst. Math. Appl. 24 (1979) 139–147] and Asymptotic approximations of integrals, Academic Press, New York, 1989. Chaps. 5, where elements of distribution theory are used, and Wong [Explicit error terms for asymptotic expansions of Mellin convolutions, J. Math. Anal. Appl. 72(2) (1979) 740–756], where, as in the present paper, the asymptotic expansions are obtained without the use of distributions. In this paper we re-derive the expansions given in Wong [Explicit error terms for asymptotic expansions of Mellin convolutions, J. Math. Anal. Appl. 72(2) (1979) 740–756] by using a different approach and we obtain new results which are not present in Wong [Explicit error terms for asymptotic expansions of Mellin convolutions, J. Math. Anal. Appl. 72(2) (1979) 740–756]: a proof of the asymptotic character of the expansions and accurate error bounds.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 200, Issue 2, 15 March 2007, Pages 628–636
نویسندگان
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