Triple simultaneous Fourier series equations involving associated Legendre function

In this paper, we have considered the two sets of triple series equations of the first kind and second kind, which are the generalization of dual series equations involving Associated Legendre functions & solved the two sets of series equations. such simultaneous Fourier equations occur in many problems in hydrodynamics, elasticity and electromagnetism, involving a spherical or spheroidal boundary when different conditions are prescribed on different parts of the boundary.