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Mathematics of Computation

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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.

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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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