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Wiener-Hopf integral equation
Let $\alpha $ be such that $0<\alpha <\frac{1}{2}$. In this note we use the Mittag-Leffler partial fractions expansion for $F_\alpha (\theta )=\Gamma \left(1-\alpha -\frac{\theta }{\pi }\right) \Gamma (\alpha )/ \Gamma \left( \alpha -\frac{\theta }{\pi }\right) \Gamma (1-\alpha )$ to obtain a solution of a Wiener-Hopf integral equation.
[1] Feller, W.: An Introduction to Probability Theory and Its Applications. Vol. II, John Wiley & Sons, New York, 1966. MR 0210154 | Zbl 0598.60003
[2] McGregor, M. T.: On a Wiener-Hopf integral equation. J. Integral Eqns. & Applns. (4)7 (1995), 475-483. MR 1382065 | Zbl 0849.45001
[3] Noble, B.: The Wiener-Hopf Technique. Pergamon Press, New York, 1958. MR 0102719 | Zbl 0657.35001
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