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

On the integral $ \int \sb{0}\sp{\pi /2}{\rm log}\sp{n}\,{\rm cos}\,x\,{\rm log}\sp{p}{\rm sin}\,x\,dx$


Author: K. S. KΓΆlbig
Journal: Math. Comp. 40 (1983), 565-570
MSC: Primary 33A35; Secondary 10H05
MathSciNet review: 689472
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Abstract | References | Similar Articles | Additional Information

Abstract: A formula is derived for the integral in the title which allows easy evaluation by formula manipulation on a computer.


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

  • [1] F. Bowman, Note on the integral ∫^{\𝑓𝑟𝑎𝑐12𝜋}(𝑙𝑜𝑔𝑠𝑖𝑛𝜃)ⁿ𝑑𝜃, J. London Math. Soc. 22 (1947), 172–173 (1948). MR 0024493 (9,503c)
  • [2] A. C. Hearn, REDUCE Users Manual, 2nd ed., Univ. of Utah, Salt Lake City, Utah, 1973.
  • [3] Peter Henrici, Applied and computational complex analysis, Wiley-Interscience [John Wiley & Sons], New York, 1974. Volume 1: Power series—integration—conformal mapping—location of zeros; Pure and Applied Mathematics. MR 0372162 (51 #8378)
  • [4] K. S. Kölbig, On the value of a logarithmic-trigonometric integral, Nordisk Tidskr. Informationsbehandling (BIT) 11 (1971), 21–28. MR 0290532 (44 #7712)
  • [5] 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)
  • [6] Yudell L. Luke, Mathematical functions and their approximations, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1975. MR 0501762 (58 #19039)
  • [7] N. Nielsen, "Der Eulersche Dilogarithmus und seine Verallgemeinerungen," Nova Acta Leopoldina, v. 90, 1909, pp. 123-211.
  • [8] N. Nielsen, "Undersøgelser over Reciproke Potenssummer og dere Anvendelse paa Raekker og Integraler," Danske Vid. Selsk. Skr., 6. Raekke, naturvid. og math. Afd., v. 8, 1898, pp. 395-443.
  • [9] N. Nielsen, "Sur la transformation d'une intégrale définie," Oversigt Danske Vid. Selsk. Forh., 1896, pp. 335-347.
  • [10] N. Nielsen, "Sur la sommation de quelques séries," Oversigt Danske Vid. Selsk. Forh., 1896, pp. 348-361.
  • [11] N. Nielsen, "Théorème sur les intégrales $ \smallint _0^{\pi /4}{\log ^p}\sin 2\phi \,d\phi $ et $ \smallint _0^{\pi /4}{\text{tg}}\,\phi {\log ^P}\sin 2\phi \,d\phi $," Oversigt Danske Vid. Selsk. Forh., 1897, pp. 197-206.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1983-0689472-3
PII: S 0025-5718(1983)0689472-3
Article copyright: © Copyright 1983 American Mathematical Society