Complete elliptic integrals of the third kind in problems of mechanics

Abstract

In the solution of many problems of mechanics and mathematical physics, there is the necessity of operating with complicated (“unbearable”) elliptic integrals of the 1st, 2nd, and 3rd kinds, in the calculation of particular values of which various programs and special tables are now used. However, the use of tables is associated with the necessity of the cross interpolation of tabular data, difficulties in programming, and the restricted scope of their application. In addition it is shown that certain tables give an inadmissibly large underestimate of the results (up to 60−80%).