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exact solutions; mixed problems; half-space; harmonic function; Integral representations

References:

[1] I. N. Sneddon: **Mixed boundary value problems in potential theory**. North-Holland Publishing Company, Amsterdam, 1966. MR 0216018 | Zbl 0139.28801

[2] T. S. Sankar V. I. Fabrikant: **Investigations of a two-dimensional integral equation in the theory of elasticity and electrostatics**. Journal de Mécanique Théorique et Appliquée, Vol. 2, No. 2, 1983, pp. 285-299. MR 0702239

[3] I. S. Gradshtein I. M. Ryzhik: **Table of Integrals, Series and Products**. AP, New York, 1965.

[4] H. Bateman A. Erdelyi: **Higher transcendental functions**. Vol. 1, McGraw-Hill, 1953. MR 0058756

[5] E. W. Hobson: **On Green's function for a circular disk, with application to electrostatic problems**. Transactions of Cambridge Philosophical Society, Vol. 18, 1900, pp. 277-291.