CONHYP swMATH ID: 152 Software Authors: Nardin, Mark; Perger, W.F.; Bhalla, Atul Description: Algorithm 707: CONHYP: A numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes A numerical evaluator for the confluent hypergeometric function for complex arguments with large magnitudes using a direct summation of Kummer’s series is presented. Extended precision subroutines using large arrays to accumulate a single numerator and denominator are ultimately used in a single division to arrive at the final result. The accuracy has been verified through a variety of tests and they show the evaluator to be consistently accurate to 13 significant figures, and on rare occasion accurate to only 9 for magnitudes of the arguments ranging into the thousands in any quadrant in the complex plane. Because the evaluator automatically determines the number of significant figures of machine precision, and because it is written in FORTRAN 77, tests on various computers have shown the evaluator to provide consistently accurate results, making the evaluator very portable. The principal drawback is that, for certain arguments, the evaluator is slow; however, the evaluator remains valuable as a benchmark even in such cases. Homepage: http://www.ece.mtu.edu/faculty/wfp/articles/acm_trans_math_soft.pdf Related Software: DLMF; FastGaussQuadrature; libcwfn; NumExp; Cephes; BIZ; AIZ; Algorithm 831; Matlab; Mathematica; SciPy; GSL; mpmath; Maple Cited in: 4 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Algorithm 707: CONHYP: A numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes. Zbl 0892.65010Nardin, Mark; Perger, W. F.; Bhalla, Atul 1992 all top 5 Cited by 11 Authors 1 Arratia, Argimiro A. 1 Bhalla, Atul 1 Gil, Amparo 1 Nardin, Mark 1 Navas-Palencia, Guillermo 1 Olver, Sheehan Shakiban 1 Pearson, John W. 1 Perger, Warren F. 1 Porter, Mason Alexander 1 Segura, Javier 1 Temme, Nico M. Cited in 3 Serials 1 ACM Transactions on Mathematical Software 1 Applied Mathematics and Computation 1 Numerical Algorithms Cited in 4 Fields 4 Special functions (33-XX) 2 Numerical analysis (65-XX) 1 Approximations and expansions (41-XX) 1 Computer science (68-XX) Citations by Year