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Efficient evaluation of the molecular auxiliary function B n by downward recursion
Author(s) -
Harris Frank E.
Publication year - 2003
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.10812
Subject(s) - recursion (computer science) , function (biology) , range (aeronautics) , value (mathematics) , mathematics , physics , combinatorics , pure mathematics , mathematical physics , quantum mechanics , statistical physics , algorithm , statistics , materials science , evolutionary biology , composite material , biology
It is known that the molecular auxiliary function B n ( q ) can be generated stably by downward recurrence for the range n > |q|, but doing so requires a starting value of B N , where N is the largest n value needed. The question of the choice of upward vs. downward recursion is revisited. Then, it is shown that by writing B N ( q ) in terms of incomplete gamma functions and introducing an asymptotic expansion for the latter the necessary starting values can be obtained far more rapidly than heretofore for a significant range of |q| and N. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
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