ANALYTICAL SOLUTIONS AND A NUMERICAL ALGORITHM FOR THE GAUSS HYPERGEOMETRIC FUNCTION (2)F(1)(A, B, C, Z)

The paper deals with the derivation of the analytical solution of a definite elliptical integral of general type which appears in fracture mechanics. The closed-form solution is expressible in terms of the Gauss hypergeometric series 2F, (a, b; c; z). As an alternative, the authors further present a suitable set of recurrence formulas and the accompanying starting solutions. Their application leads to other closed-form expressions for the elliptical integral which are offered in the Appendix. Therefore, as a new result, analytical expressions are given for the Gauss hypergeometric series 2F1 (a, b; c; z) for specific parameters a, b, c. A powerful algorithm for the numerical computation of 2F1 has been developed.