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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Closed expressions for $\int ^{1}_{0}t^{-1}\textrm {log}^{n-1}\ t\log ^{p}(1-t) dt$
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by K. S. Kölbig PDF
Math. Comp. 39 (1982), 647-654 Request permission


Closed expressions for the integral $\smallint _0^1{t^{ - 1}}{\log ^{n - 1}}t{\log ^p}(1 - t)\;dt$, whose general form is given elsewhere, are listed for $n = 1(1)9$, $p = 1(1)9$. A formula is derived which allows an easy evaluation of these expressions by formula manipulation on a computer.
    J. A. Fox & A. C. Hearn, "Analytic computation of some integrals in fourth order quantum electrodynamics," J. Comput. Phys., v. 14, 1974, pp. 301-317. I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series and Products, Academic Press, New York, 1980. A. C. Hearn, REDUCE Users Manual, 2nd ed., Univ. of Utah, Salt Lake City, Utah, 1973. K. S. Kölbig, J. A. Mignaco & E. Remiddi, "On Nielsen’s generalized polylogarithms and their numerical calculation," BIT, v. 10, 1970, pp. 38-74.
  • K. S. Kölbig, On the value of a logarithmic-trigonometric integral, Nordisk Tidskr. Informationsbehandling (BIT) 11 (1971), 21–28. MR 290532, DOI 10.1007/bf01935325
  • Leonard Lewin, Polylogarithms and associated functions, North-Holland Publishing Co., New York-Amsterdam, 1981. With a foreword by A. J. Van der Poorten. MR 618278
  • Wilhelm Maier and Helmut Kiesewetter, Funktionalgleichungen mit analytischen Lösungen, Studia Mathematica/Mathematische Lehrbücher, Band XX, Vandenhoeck & Ruprecht, Göttingen-Zurich, 1971 (German). MR 0324007
  • D. Maison & A. Petermann, "Subtracted generalized polylogarithms and the SINAC program," Comput. Phys. Comm., v. 7, 1974, pp. 121-134. N. Nielsen, "Der Eulersche Dilogarithmus und seine Verallgemeinerungen," Nova Acta Leopoldina, v. 90, 1909, pp. 123-211.
  • T. J. Stieltjes, Table des valeurs des sommes $S_k=\sum \limits _1^\infty n^{-k}$, Acta Math. 10 (1887), no. 1, 299–302 (French). MR 1554740, DOI 10.1007/BF02393705
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 39 (1982), 647-654
  • MSC: Primary 33A70; Secondary 33-04
  • DOI:
  • MathSciNet review: 669656