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Computation of auxiliary functions in STO molecular integrals up to arbitrary accuracy. I. evaluation of incomplete gamma function E n ( x ) by forward recursion
Author(s) -
Li Yanxin,
Dong Xialan,
Pan Shoufu
Publication year - 1993
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560450103
Subject(s) - recursion (computer science) , computation , function (biology) , mathematics , approximation error , relation (database) , error function , algorithm , computer science , database , evolutionary biology , biology
Abstract A new inequality and an approximate relation of incomplete Gamma function E n ( x ) are derived in this paper. Applying both to simplify the error analysis on the recursive algorithm of E n ( x ), we analytically derived a criterion about relative error. The criterion decides whether the forward recursive relation can be used to compute { E n ( x ), n = 0, 1, ⃛, N } with an acceptable loss of significant figures. Further analytical exploration leads to another criterion that decides whether the group of E n ( x ) can be evaluated with an acceptable absolute error by the same methods. Both criteria are not only superior to those given in previous work by other authors, but also strongly supported by our numerical experiments. A strategy is illustrated to explain how to apply both criteria to evaluate molecular integral over Slater‐type orbitals. © 1993 John Wiley & Sons, Inc.