Algorithm 413: ENTCAF and ENTCRE

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Algorithm 413: ENTCAF and ENTCRE: evaluation of normalized Taylor coefficients of an analytic function

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Communications of the ACM archive
Volume 14 , Issue 10 (October 1971) table of contents

Pages: 669 - 675

Year of Publication: 1971

ISSN:0001-0782

Authors

J. N. Lyness	Argonne National Laboratory, Argonne, IL
G. Sande	Univ. of Chicago, IL

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 4, Downloads (12 Months): 25, Citation Count: 3

Additional Information:

appendices and supplements references cited by index terms collaborative colleagues

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APPENDICES and SUPPLEMENTS

ENTCRE (413.gz) (8 KB)

taylor series coefficient by contour integration

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	Delves, L.M., and Lyness, J.N. A numerical method for locating the zeros of an analytic function. Math. Comput. 21 (1967), 543-560.
	2	Walter Gautschi , Bruce J. Klein, Recursive computation of certain derivatives&a study of error propagation, Communications of the ACM, v.13 n.1, p.7-9, Jan. 1970 [doi>10.1145/361953.361959]
	3	Walter Gautschi , Bruce J. Klein, Remark on algorithm 282 [S22] derivatives of ex/x, cos(x)/x, and sin (x)/x, Communications of the ACM, v.13 n.1, p.53-54, Jan. 1970 [doi>10.1145/361953.361988]
	4	Gentleman, W.M., and Sande, G. Fast Fourier transformsfor fun and profit. Proc. AFIP$ 1966 FJCC, Vol. 29, Spartan Books, New York, pp. 563-578.
	5	Lyness, J.N., and Delves, L.M. On numerical contour integration round a closed contour. Math. Comput. 21 (1967), 561-577.
	6	Lyness, J.N., and Moler, C.B., Numerical differentiation of analytic functions. SIAM J. Numer. Anal. 4 (1967), 202-210.
	7	J. N. Lyness, Numerical algorithms based on the theory of complex variable, Proceedings of the 1967 22nd national conference, p.125-133, January 1967, Washington, D.C., United States [doi>10.1145/800196.805983]
	8	Lyness, J.N. Quadrature methods based on complex function values. Math. Comput. 23 (1969), 601-620.
	9	Sande, G., Fast Fourier transform--A globaly complex algorithm with locally real implementation. Proc. 4th Ann. Princeton Symp. on Information Sciences and Systems, 1970, pp. 136-142.

CITED BY 3

	Bengt Fornberg, Numerical Differentiation of Analytic Functions, ACM Transactions on Mathematical Software (TOMS), v.7 n.4, p.512-526, Dec. 1981
	B. S. Garbow , G. Giunta , J. N. Lyness , A. Murli, Software for an implementation of Weeks' method for the inverse Laplace transform, ACM Transactions on Mathematical Software (TOMS), v.14 n.2, p.163-170, June 1988
	B. S. Garbow , G. Giunta , J. N. Lyness , A. Murli, ALGORITHM 662: a Fortran software package for the numerical inversion of the Laplace transform based on Weeks' method, ACM Transactions on Mathematical Software (TOMS), v.14 n.2, p.171-176, June 1988

INDEX TERMS

Keywords:
Cauchy integral, Taylor coefficients, Taylor series, complex arithmetic, complex variable, fast Fourier transform, interpolation, numerical differentiation, numerical integration

Collaborative Colleagues:

J. N. Lyness: colleagues

G. Sande: colleagues

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