|
(1) |
where is the Riemann Zeta Function and is the Gamma Function (Gradshteyn and Ryzhik
1980, 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 by
|
(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.
© 1996-9 Eric W. Weisstein
1999-05-20