Algorithm 707: CONHYP: a numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes

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Algorithm 707: CONHYP: a numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 18 , Issue 3 (September 1992) table of contents

Pages: 345 - 349

Year of Publication: 1992

ISSN:0098-3500

Authors

Mark Nardin	University of Michigan, Ann Arbor
W. F. Perger	Michigan Technological University
Atul Bhalla	Michigan Technological University

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 5, Downloads (12 Months): 76, Citation Count: 2

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appendices and supplements abstract references cited by index terms collaborative colleagues peer to peer

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APPENDICES and SUPPLEMENTS

CONHYP (707.gz) (7 KB)

confluent hypergeometric function
Gams: c1

ABSTRACT

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.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	Mark Nardin , W. F. Perger , Atul Bhalla, Numerical evaluation of the confluent hypergeometric function for complex arguments of large magnitudes, Journal of Computational and Applied Mathematics, v.39 n.2, p.193-200, March 30, 1992 [doi>10.1016/0377-0427(92)90129-L]
	2	Milton Abramowitz, Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,, Dover Publications, Incorporated, 1974
	3	SLATER, L.J. Confluent Hypergeometric Functions. Cambridge University Press, London, 1960, 58-60.

CITED BY 2

	Yalin Xiong , Steven A. Shafer, Hypergeometric Filters for Optical Flow and Affine Matching, International Journal of Computer Vision, v.24 n.2, p.163-177, Sept. 1997
	Yalin Xiong , Steven A. Shafer, Moment and Hypergeometric Filters for High Precision Computation ofFocus, Stereo and Optical Flow, International Journal of Computer Vision, v.22 n.1, p.25-59, Feb./March 1997