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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 some trigonometric integrals
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by Henry E. Fettis PDF
Math. Comp. 35 (1980), 1325-1329 Request permission

Abstract:

Expressions are obtained for the integrals \[ I_\lambda ^{(p)} = \int _0^{\pi /2}{\left ( {\frac {{\sin \lambda \theta }}{{\sin \theta }}} \right )^p}d\theta ,\quad J_\lambda ^{(p)} = \int _0^{\pi /2}{\left ( {\frac {{1 - \cos \lambda \theta }}{{\sin \theta }}} \right )^p}d\theta \] for arbitrary real values of "$\lambda$", and $p = 1,2$.
References
    I. S. GRADSHTEYN & I. M. RYZHIK, Table of Integrals, Series and Products, Academic Press, New York, 1965.
  • Wilhelm Magnus and Fritz Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, Springer-Verlag, Berlin, 1948 (German). 2d ed. MR 0025629
  • J. EDWARDS, A Treatise on the Integral Calculus, Vol. II, Macmillan, New York, 1922; reprinted by Chelsea, New York, 1977.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1325-1329
  • MSC: Primary 33A15; Secondary 33A10, 33A70
  • DOI: https://doi.org/10.1090/S0025-5718-1980-0583510-1
  • MathSciNet review: 583510