On a new transformation formula for bilateral _6{\psi }_6 series and applications
In this paper, we derive a new transformation formula for bilateral \(_6\psi _6\) series using Roger’s \(_6\phi _5\) summation and then use it to deduce the well-known Bailey’s \(_6\psi _6\) summation formula. Also, we deduce some identities involving theta functions and new identities analogous to identities of Ramanujan. Further, we give formulas for finding the number of representations of an integer as sums of squares and sums of triangular numbers.
In this paper we study the deformation of right porous cylinders subjected to a prescribed thermal field. We assume that the cylinder is filled by an inhomogeneous anisotropic porous material. In the first part of the paper we study the problem of extension-bending-torsion, when the thermal field is independent of the axial coordinate and then we study the problem of extension-bending-torsion-flexure when the thermal field is considered linear in the axial coordinate. The considered problems are reduced to some generalized plane strain problems in the cross-section of the cylinder. Our analysis shows how the considered thermal fields influence the deformation of the porous cylinders.