“Xi Function”的概念、定义、习题解题方法及翻译-数学辞典

单词

Xi Function

释义

Xi Function

(1)

where

is the Riemann Zeta Function and

is the Gamma Function (Gradshteyn and Ryzhik1980, p. 1076). The

function satisfies the identity

(2)

The zeros of

and of its Derivatives are all located on the Critical Strip

,where

. Therefore, the nontrivial zeros of the Riemann Zeta Function exactly correspond to those of

. The function

is related to what Gradshteyn and Ryzhik (1980, p. 1074) call

(3)

where

. This function can also be defined as

(4)

giving

(5)

The de Bruijn-Newman Constant is defined in terms of the

function.

See also de Bruijn-Newman Constant

References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, corr. enl. 4th ed. San Diego, CA: Academic Press, 1980.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。