New double-sided bounds for complete elliptic integrals of the first and the second kinds

Two theorems are proved in this paper, in which lower and upper bounds are established for complete elliptic integrals of the first and second kind, expressed in terms of elementary functions. These theorems are applied to a model geometric example. In addition, the article presents graphs of dependencies on the modulus of these integrals of both the estimates obtained and their relative errors. The applicability of the approximations found for technical applications is also discussed.