The new complete orthonormal sets of exponential-type orbitals (ETOs) are introduced in closed form as functions of the exponential, the complex or real regular solid spherical harmonic, and the generalized Laguerre polynomials, Psi(nml)(alpha/)(zeta,(r) over right arrow) = (-1)(alpha) [(2zeta)(3)(n-l-1)!/(2n)(alpha)[(n+l-alpha)!(3)](1/2) (2zetar)(l)e(-zetarL2l=2-alpha)/(n+l+1-alpha) (2zetar)S-lm(theta,phi), where alpha = 1,0,-1,-2,-3,.... These Psi(alpha)-ETOs are represented as finite linear combinations of Slater-type orbitals (STOs). The Coulomb Sturmian and Lambda ETOs are the special classes of Psi(alpha)-ETOs for alpha = 1 and alpha = 0, respectively. By the use of Psi(alpha)-ETOs the simpler expansion formulas for translation of STOs are derived. The translation coefficients are presented by a linear combination of overlap integrals. The final results are especially useful for machine computations of arbitrary multielectron multicenter molecular integrals over STOs that arise in the Hartree-Fock-Roothaan approximation and also in the Hylleraas correlated wave function method which play a significant role in theory and application to quantum mechanics of atoms, molecules, and solids. (C) 2002 Wiley Periodicals, Inc. Int.