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Mathematics of Computation

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On some trigonometric integrals

Author: Henry E. Fettis
Journal: Math. Comp. 35 (1980), 1325-1329
MSC: Primary 33A15; Secondary 33A10, 33A70
Corrigendum: Math. Comp. 37 (1981), 605.
Corrigendum: Math. Comp. 37 (1981), 605.
MathSciNet review: 583510
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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 [Enhancements On Off] (What's this?)

    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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Keywords: Integrals, definite integrals, trigonometric integrals, Gamma function, Psi function
Article copyright: © Copyright 1980 American Mathematical Society