SOME IDENTITIES FOR THE RIEMANN ZETA-FUNCTION II

被引：0
|
作者：
Ivic, Aleksandar [1 ,2 ]
机构：
[1] Univ Beogradu, Katedra Matemat RGF, Dusina 7, Beograd 11000, Serbia
[2] Univ Beogradu, Katedra Matemat RGF, Beograd 11000, Montenegro
来源：
FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS | 2005年 / 20卷
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D O I：
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中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Several identities for the Riemann zeta-function zeta(s) are proved. For example, if (sic)(1) (x) := {x} = x - [x], (sic)(n)(x) := integral(+infinity)(0){u} (sic)(n -1) (x/u) du/u (n >= 2), then zeta(n) (s)/(-s)(n) = integral(+infinity)(0) (sic)n(x)(x-1-s) dx (s = sigma + it, 0 < sigma < 1) and 1/2 pi integral(+infinity)(-infinity) vertical bar zeta(sigma + it)vertical bar(2n) / (sigma(2) + it)(n) dt = integral(+infinity)(0) (sic)(2)(n)(x)x(-1-s-2 sigma) dx (0 < sigma < 1).
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页码：1 / 8
页数：8
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