On certain Schlِmilch-type series

By using a form of the Poisson summation formula together with a generalization due to Srivastava and Exton of the discontinuous integral of Weber and Schafheitlin and the (heretofore not readily available) cosine transform of the hypergeometric function 1F2[−b2t2] (b > 0), several new Schlömilch and Fourier-type series are evaluated. By specialization of the latter series numerous results appearing in the literature are obtained in a unified way.