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More trigonometric integrals

Author: Henry E. Fettis
Journal: Math. Comp. 43 (1984), 557-564
MSC: Primary 33A10; Secondary 26A42
MathSciNet review: 758203
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Abstract: Integrals of the form

$\displaystyle \int_0^{\pi /2} {{e^{ip\theta }}{{\cos }^q}\theta \,d\theta ,\quad \int_0^{\pi /2} {{e^{ip\theta }}{{\sin }^q}\theta \,d\theta } } $

(p real, $ \operatorname{Re} (q) > - 1$) are expressed in terms of Gamma and hypergeometric functions for integer and noninteger values of q and p. The results include those of [2] as special cases.

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

  • [1] I. S. Gradshteyn & I. M. Ryzhik, Table of Integrals, Series and Products, corrected and enlarged edition, Academic Press, New York, 1980. MR 582453 (81g:33001)
  • [2] H. E. Fettis, "On some trigonometric integrals," Math. Comp., v. 35, 1980, pp. 1325-1329. MR 583510 (82c:33003a)
  • [3] M. Abramowitz & I. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965.
  • [4] W. Magnus & F. Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, Springer-Verlag, Berlin, 1948. MR 0025629 (10:38a)
  • [5] G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed., reprinted, Cambridge Univ. Press, New York and London, 1966. MR 1349110 (96i:33010)

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Keywords: Integrals, definite integrals, Gamma functions, hypergeometric functions, Psi functions
Article copyright: © Copyright 1984 American Mathematical Society

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