کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4645493 | 1632211 | 2010 | 9 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Asymptotic and factorial expansions of Euler series truncation errors via exponential polynomials
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات محاسباتی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
A detailed analysis of the remainder obtained by truncating the Euler series up to the nth-order term is presented. In particular, by using an approach recently proposed by Weniger, asymptotic expansions of the remainder, both in inverse powers and in inverse rising factorials of n, are obtained. It is found that the corresponding expanding coefficients are expressed, in closed form, in terms of exponential polynomials, well known in combinatorics, and in terms of associated Laguerre polynomials, respectively. A study of the divergence and/or of the convergence of the above expansions is also carried out for positive values of the Euler series argument.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Numerical Mathematics - Volume 60, Issue 12, December 2010, Pages 1242-1250
Journal: Applied Numerical Mathematics - Volume 60, Issue 12, December 2010, Pages 1242-1250