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Analytical Solutions and a Numerical Algorithm for the Gauss's Hypergeometric Function 2 F 1 (a, b; c; z)
Author(s) -
Mayrhofer K.,
Fischer F. D.
Publication year - 1994
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19940740709
Subject(s) - gauss , hypergeometric function , mathematics , generalized hypergeometric function , computation , series (stratigraphy) , function (biology) , hypergeometric distribution , mathematical analysis , confluent hypergeometric function , type (biology) , algorithm , pure mathematics , physics , quantum mechanics , paleontology , ecology , evolutionary biology , biology
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 2 F 1 (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 2 F 1 (a, b; c; z) for specific parameters a, b, c. A powerful algorithm for the numerical computation of 2 F 1 has been developed.