  The Ramanujan zeta function was in $1916$ proposed by an Indian mathematician
Srinivasa Ramanujan. As an analogue of the Riemann hypothesis, an English
mathematician Godfrey Harold Hardy proposed in $1940$ that the real part of all
complex zeros of the Ramanujan zeta function is $6$. This is the well-known
Riemann-Hardy hypothesis for the Ramanujan zeta function. This article is
devoted to the proof of this hypothesis derived from the Ramanujan-Rankin
function. Owing to the integral representation of the Ramanujan-De Bruijn
function, we establish its series. We also reduce its product using the
Hadamard's factorization theorem. By a class with its series and product
representations, we conclude that the real part of all zeros for Ramanujan-De
Bruijn function is zero. we also obtain its products of Conrey and Ghosh and
Hadamard-type for the Ramanujan-Rankin function. Based on the obtained result,
we prove that the Riemann-Hardy hypothesis is true.
