کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10149831 | 1646775 | 2018 | 34 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Sums of squares and products of Bessel functions
ترجمه فارسی عنوان
مجموع مربعات و محصولات توابع بسل
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
Let rk(n) denote the number of representations of the positive integer n as the sum of k squares. We rigorously prove for the first time a Voronoï summation formula for rk(n),kâ¥2, proved incorrectly by A.I. Popov and later rediscovered by A.P. Guinand, but without proof and without conditions on the functions associated in the transformation. Using this summation formula we establish a new transformation between a series consisting of rk(n) and a product of two Bessel functions, and a series involving rk(n) and the Gaussian hypergeometric function. This transformation can be considered as a massive generalization of well-known results of G.H. Hardy, and of A.L. Dixon and W.L. Ferrar, as well as of a classical result of A.I. Popov that was completely forgotten. An analytic continuation of this transformation yields further useful results that generalize those obtained earlier by Dixon and Ferrar.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 338, 7 November 2018, Pages 305-338
Journal: Advances in Mathematics - Volume 338, 7 November 2018, Pages 305-338
نویسندگان
Bruce C. Berndt, Atul Dixit, Sun Kim, Alexandru Zaharescu,