To calculation of full elliptic integrals third sortsin applied researches

Abstract

Introduction. When carrying out theoretical and applied researches on modeling of hydrogeophysical filtrational processes and other potential streams quite often there is a need of analytical determination of values of “impossible” elliptic integrals that is connected with labor-consuming mathematical calculations, cross nonlinear interpolating of these special tables and schedules, etc. Use at the solution of applied tasks for their definition of computer programs yields only discrete results in “figures” (but not in “symbols”) without a possibility of their subsequent transformations for receiving the common analytical decision in elementary functions.
 
 Materials and methods. Therefore, despite existence of various computing programs, analytical decisions are demanded so far as they have great opportunities for identification of internal physical relationships of cause and effect in solvable tasks and the subsequent their use in mathematical transformations.
 
 Results. In work estimated dependences in elementary functions by determination of values of full elliptic integral 3rd sorts with a sufficient accuracy (~ << 2–4 %) for carrying out applied (and theoretical) researches are offered. 
 
 Conclusions. L. Milne-Thomson is brought comparison of the received results with exact data of the Mathcad program for a wide interval of changes of parameter of integral and theoretical decisions.