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The article develops and proves an exponentially convergentnumerical-analytical method (the FD-method) for solving Sturm-Liouvilleproblems with a singular Legendre operator and a singular potential. Obtainedwithin are sufficient conditions for convergence of the method and a prioriestimates of its accuracy. A detailed algorithm for programmatic implementationof the FD-method is presented and compared with known algorithms (SLEIGN2).

Exponentially convergent numerical-analytical method for solving eigenvalue problems for singular differential operators