A representation of Linnik's Probability Densities by a contour integral distinct than the one given in  is obtained. An Improper integral representation of the same density functions is derived. An investigation into the exceptional set is achieved as well.
HAYFAVİ, A. (BASTIYALI) (1998) "An Improper Integral Representation of Linnik's Probability Densities," Turkish Journal of Mathematics: Vol. 22: No. 2, Article 11. Available at: https://journals.tubitak.gov.tr/math/vol22/iss2/11