Skip to main content
SpringerLink
Log in

A Fast Algorithm for Computing the Digamma Function

  • THEMATIC ISSUE
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

A fast algorithm for calculating the logarithmic derivative of the Euler gamma function based on the BVE method is constructed. The complexity of the algorithm is close to optimal. The structure of the algorithm allows its parallelization.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. Dynkin, E.B., Kolmogorov, A.N., Kostrikin, A.I., et al., Six Lectures Delivered at the International Congress of Mathematicians in Stockholm, 1962 , series 2 of American Mathematical Society Translations, Providence, Am. Math. Soc., 1963, vol. 31.

  2. Karatsuba, A.A., Complexity of calculations, Proc. Steklov Inst. Math., 1995, vol. 211, pp. 169–183.

    Google Scholar 

  3. Karatsuba, A. and Ofman, Yu., Multiplying multidigit numbers on automata, Dokl. Akad. Nauk SSSR, 1962, vol. 145, no. 2, pp. 293–294.

    Google Scholar 

  4. Schönhage, A. and Strassen, V., Schnelle Multiplikation großer Zahlen, Computing, 1971, no. 7, pp. 281–292.

  5. Fürer, M., Faster integer multiplication, SIAM J. Comput., 2009, vol. 39, no. 3, pp. 979–1005.

  6. Benderskii, Yu.V., Fast computation, Dokl. Akad. Nauk SSSR, 1975, vol. 223, no. 5, pp. 1041–1043.

    MathSciNet  Google Scholar 

  7. Salamin, Е., Computation of \(\pi \) using arithmetic-geometric mean, Math. Comput., 1976, vol. 30, no. 135, pp. 565–570.

    MathSciNet  MATH  Google Scholar 

  8. Carlson, B.C., Algorithms involving arithmetic and geometric means, Am. Math. Mon., 1971, no. 78, pp. 496–505.

  9. Borwein, J.M. and Borwein, P.B., Pi and the AGM—A Study in Analytic Number Theory and Computational Complexity, New York: Wiley, 1987.

    MATH  Google Scholar 

  10. Karatsuba, E.A., Fast computation of transcendental functions, Probl. Peredachi Inf., 1991, vol. 27, no. 4, pp. 76–99.

    MathSciNet  MATH  Google Scholar 

  11. Karatsuba, E.A., Calculation of Bessel functions via the summation of series, Numer. Anal. Appl., 2019, vol. 12, no. 4, pp. 372–387.

    Article  MathSciNet  Google Scholar 

  12. Lozier, D.W. and Olver, F.W.J., Numerical evaluation of special functions, in Mathematics of Computation 1943–1993: A Half -Century of Computational Mathematics. Proc. Symp. Appl. Math., Gautschi, W., Ed., Providence: Am. Math. Soc., 1994, no. 48, pp. 79–125.

  13. Siegel, C.L., Transcendental Numbers, Princeton: Princeton Univ. Press, 1949.

    MATH  Google Scholar 

  14. Temme, N.M., Special Functions. An Introduction to the Classical Functions of Mathematical Physics, New York: John Wiley and Sons, 1996.

    Book  MATH  Google Scholar 

  15. Karatsuba, Е.А., On the computation of the Euler constant \(\gamma \), Numer. Algorithms, 2000, no. 24, pp. 83–97.

  16. Bach, Е., The complexity of number-theoretic constants, Inf. Process. Lett., 1997, no. 62, pp. 145–152.

Download references

Funding

This work was supported by the Russian Science Foundation, project no. 22-21-00727.

Author information

Authors and Affiliations

  1. Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia

    E. A. Karatsuba

Authors
  1. E. A. Karatsuba
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. A. Karatsuba.

Additional information

Translated by V. Potapchouck

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karatsuba, E.A. A Fast Algorithm for Computing the Digamma Function. Autom Remote Control 83, 1576–1589 (2022). https://doi.org/10.1134/S00051179220100101

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S00051179220100101

Keywords

Search

Navigation