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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Closed expressions for $ \int \sp{1}\sb{0}t\sp{-1}{\rm log}\sp{n-1}\ t\log\sp{p}(1-t)\,dt$


Author: K. S. KΓΆlbig
Journal: Math. Comp. 39 (1982), 647-654
MSC: Primary 33A70; Secondary 33-04
MathSciNet review: 669656
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Abstract: 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.


References [Enhancements On Off] (What's this?)

  • [1] 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.
  • [2] I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series and Products, Academic Press, New York, 1980.
  • [3] A. C. Hearn, REDUCE Users Manual, 2nd ed., Univ. of Utah, Salt Lake City, Utah, 1973.
  • [4] K. S. Kölbig, J. A. Mignaco & E. Remiddi, "On Nielsen's generalized polylogarithms and their numerical calculation," BIT, v. 10, 1970, pp. 38-74.
  • [5] K. S. Kölbig, On the value of a logarithmic-trigonometric integral, Nordisk Tidskr. Informationsbehandling (BIT) 11 (1971), 21–28. MR 0290532 (44 #7712)
  • [6] Leonard Lewin, Polylogarithms and associated functions, North-Holland Publishing Co., New York, 1981. With a foreword by A. J. Van der Poorten. MR 618278 (83b:33019)
  • [7] Wilhelm Maier and Helmut Kiesewetter, Funktionalgleichungen mit analytischen Lösungen, Vandenhoeck & Ruprecht, Göttingen, 1971 (German). Studia Mathematica/Mathematische Lehrbücher, Band XX. MR 0324007 (48 #2359)
  • [8] D. Maison & A. Petermann, "Subtracted generalized polylogarithms and the SINAC program," Comput. Phys. Comm., v. 7, 1974, pp. 121-134.
  • [9] N. Nielsen, "Der Eulersche Dilogarithmus und seine Verallgemeinerungen," Nova Acta Leopoldina, v. 90, 1909, pp. 123-211.
  • [10] T. J. Stieltjes, Table des valeurs des sommes 𝑆_{𝑘}=∑\𝑙𝑖𝑚𝑖𝑡𝑠₁^{∞}𝑛^{-𝑘}, Acta Math. 10 (1887), no. 1, 299–302 (French). MR 1554740, http://dx.doi.org/10.1007/BF02393705

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1982-0669656-X
PII: S 0025-5718(1982)0669656-X
Article copyright: © Copyright 1982 American Mathematical Society