On the zeros of certain trigonometric integrals. (English) Zbl 0642.30004
Integrals of the form \(\int^{1}_{0}\phi (t) \cos zt dt\) are discussed. The condition on \(\phi\) is less restrictive than in the existing literature. A particular example, related to Gauss hypergeometric functions, is considered in detail, with a proof based on the argument principle.
Reviewer: N.M.Temme
MSC:
| 30C15 | Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) |
| 33C05 | Classical hypergeometric functions, \({}_2F_1\) |
| 41A60 | Asymptotic approximations, asymptotic expansions (steepest descent, etc.) |
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