کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4594881 1335786 2009 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The hyperelliptic integrals and π
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
The hyperelliptic integrals and π
چکیده انگلیسی

TextA class of hyperelliptic integrals are expressed through hypergeometric functions, like those of Gauss, Lauricella and Appell, namely multiple power series. Whenever they can on their own be reduced to elliptic integrals through an algebraic transformation, we obtain a two-fold representation of the same mathematical object, and then several completely new π determinations through the above special functions and/or Euler integrals. All our π formulae have been successfully tested by means of convenient Mathematica®'s packages and enter in a wide historical/sound context of π-formulae quite far from being exhausted. Due to their structure, the formulae's practical value does not lie in computing π, but in allowing, through π, a benchmark for computing the involved special functions, particularly those less elementary.VideoFor a video summary of this paper, please visit http://www.youtube.com/watch?v=UHZIHgAeCUc.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 129, Issue 12, December 2009, Pages 3094–3108
نویسندگان
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