A new identity involving positive roots of bessel functions of the first kind

A new identity, namely sum;+∞n=1{∫01ydv(λnY)dyJv+1(λn)}2=122(v⩾0) posed, where Jv(z) is a Bessel function of the first kind of order v, and αn is the nth positive zero of Jv(z). It is shown that the formula can be used to find an upper bound for some integrals. Special cases of the series are discussed as well.