کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4607677 1337877 2011 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The Möbius inversion formula for Fourier series applied to Bernoulli and Euler polynomials
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
The Möbius inversion formula for Fourier series applied to Bernoulli and Euler polynomials
چکیده انگلیسی

Hurwitz found the Fourier expansion of the Bernoulli polynomials over a century ago. In general, Fourier analysis can be fruitfully employed to obtain properties of the Bernoulli polynomials and related functions in a simple manner. In addition, applying the technique of Möbius inversion from analytic number theory to Fourier expansions, we derive identities involving Bernoulli polynomials, Bernoulli numbers, and the Möbius function; this includes formulas for the Bernoulli polynomials at rational arguments. Finally, we show some asymptotic properties concerning the Bernoulli and Euler polynomials.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 163, Issue 1, January 2011, Pages 22–40
نویسندگان
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