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

 

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 | References | Similar Articles | Additional Information

Abstract: Expressions are obtained for the integrals

$\displaystyle I_\lambda ^{(p)} = \int _0^{\pi /2}{\left( {\frac{{\sin \lambda \... ...}{\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?)

  • [1] I. S. GRADSHTEYN & I. M. RYZHIK, Table of Integrals, Series and Products, Academic Press, New York, 1965.
  • [2] Wilhelm Magnus and Fritz Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, Springer-Verlag, Berlin, 1948 (German). 2d ed. MR 0025629 (10,38a)
  • [3] 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

DOI: http://dx.doi.org/10.1090/S0025-5718-1980-0583510-1
PII: S 0025-5718(1980)0583510-1
Keywords: Integrals, definite integrals, trigonometric integrals, Gamma function, Psi function
Article copyright: © Copyright 1980 American Mathematical Society