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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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On the integral $\int _{0}^{\pi /2}\textrm {log}^{n} \textrm {cos} x \textrm {log}^{p}\textrm {sin} x dx$
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by K. S. Kölbig PDF
Math. Comp. 40 (1983), 565-570 Request permission

Abstract:

A formula is derived for the integral in the title which allows easy evaluation by formula manipulation on a computer.
References
  • F. Bowman, Note on the integral $\int ^{\frac 12 \pi }(\rm log\,sin\theta )^nd\theta$, J. London Math. Soc. 22 (1947), 172–173 (1948). MR 24493, DOI 10.1112/jlms/s1-22.3.172
  • A. C. Hearn, REDUCE Users Manual, 2nd ed., Univ. of Utah, Salt Lake City, Utah, 1973.
  • Peter Henrici, Applied and computational complex analysis, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. Volume 1: Power series—integration—conformal mapping—location of zeros. MR 0372162
  • 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
  • Yudell L. Luke, Mathematical functions and their approximations, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0501762
  • N. Nielsen, "Der Eulersche Dilogarithmus und seine Verallgemeinerungen," Nova Acta Leopoldina, v. 90, 1909, pp. 123-211. 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. N. Nielsen, "Sur la transformation d’une intégrale définie," Oversigt Danske Vid. Selsk. Forh., 1896, pp. 335-347. N. Nielsen, "Sur la sommation de quelques séries," Oversigt Danske Vid. Selsk. Forh., 1896, pp. 348-361. 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
  • © Copyright 1983 American Mathematical Society
  • Journal: Math. Comp. 40 (1983), 565-570
  • MSC: Primary 33A35; Secondary 10H05
  • DOI: https://doi.org/10.1090/S0025-5718-1983-0689472-3
  • MathSciNet review: 689472