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A Computational Procedure for Incomplete Gamma Functions

Editor: John R. Rice Author:

Walter GautschiAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 5, Issue 4

Pages 466 - 481

https://doi.org/10.1145/355853.355863

Published: 01 December 1979 Publication History

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References

[1]

ABRAMOWITZ, M., AND STEGUN, I.A., EDS. Handbook of Mathematical Functions. Nat. Bur. Standards Appl. Math. Series 55, U.S. Govt. Printing Office, 1964.

Google Scholar

[2]

GAUTSCHI, W. Algorithm 542. Incomplete gamma functions. ACM Trans. Math. Software 5, 4 (Dec. 1979), 482-489.

Crossref

Google Scholar

[3]

GAUTSCHI, W. An evaluation procedure for incomplete gamma functions. MRC Tech. Summary Rep. 1717, Mathematics Res. Ctr., U. of Wisconsin, Madison, Feb. 1977.

Google Scholar

[4]

GAUTSCHI, W Anomalous convergence of a continued fraction for ratios of Kummer functions. Math. Comp. 31 (1977), 994-999.

Google Scholar

[5]

GAUTSCHI, W Zur Numerlk rekurrenter Relatlonen. Comptg. 9 (1972), 107-126. (English translation m Aerospace Res. Lab. Rep. ARL 73-0005, Wright Patterson AFB, Feb. 1973.)

Google Scholar

[6]

KHAMIS, S H. Tables of the incomplete Gamma Functzon Ratto. Justus yon Lieblg Verlag, Darmstadt, 1965.

Google Scholar

[7]

KOTANI, M., AMENIYA, A., ISHIGURO, E., AND KIMURA, T. Table of Molecular Integrals. Maruzen Co, Ltd., Tokyo, 1955

Google Scholar

[8]

MILLER, J., GERHAUSEN, J.M., AND MATSEN, F.A. Quantum Chemistry Integrals and Tables U. of Texas Press, Austin, 1959.

Google Scholar

[9]

PAGUROVA, V I. Tables of the Exponenttal Integral E,.(x) = ~ e-~Uu-'' du. (Translated from the Russian by D. G. Fry), Pergamon Press, New York, 1961.

Google Scholar

[10]

PEARSON, K., Ed., Tables of the Incomplete DFunct~on Biometrika Office, U. College, Cambridge U. Press, Cambridge, 1934.

Google Scholar

[11]

PERRO~, O. Die Lehre yon den Kettenbruchen, Vol. II, 3rd ed., B.G. Teubner, Stuttgart, 1957.

Google Scholar

[12]

TEMME, N.M. The asymptotic expansion of the incomplete gamma functions. Rep. TW 165/77, Stichting Mathematisch Centrum, Amsterdam, 1977.

Google Scholar

[13]

TRICOMI, F.G. Funzloni ipergeometnche confluenti. Edizioni Cremonese, Rome, 1954.

Google Scholar

[14]

TRICOMI, F.G. Sulla funzlone gamma mcompleta. Ann. Mat. Pura Appl. (4) 31 (1950), 263-279.

Google Scholar

[15]

WALL, H.S. Analytw Theory of Contmued Fractions Van Nostrand, New York, 1948. (Reprinted in 1967 by Chelsea Publ Co., Bronx, N.Y )

Google Scholar

[16]

WRENCH, J.W., JR. Concermng two series for the gamma function. Math. Comp. 22 (1968), 617- 626.

Google Scholar

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Index Terms

A Computational Procedure for Incomplete Gamma Functions
1. Mathematics of computing
  1. Mathematical analysis
    1. Functional analysis
      1. Approximation
  2. Probability and statistics
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis

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Published In

ACM Transactions on Mathematical Software Volume 5, Issue 4

Dec. 1979

153 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/355853

Editor:
John R. Rice

Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 December 1979

Published in TOMS Volume 5, Issue 4

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Extended matrix variate gamma and beta functions

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Extended matrix variate gamma and beta functions

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