Abstract
The fourth-order partial differential equation for the biharmonic Poisson integral is presented in the case of the upper half-plane (y > 0). To solve this equation, two boundary conditions must be taken into account. The boundary-value problem is solved by transforming the presented boundary-value problem for the biharmonic Poisson integral into two boundary-value problems for some two-dimensional functions A(q, y) and B (q, y). After that, the biharmonic Poisson integral for the upper half-plane is obtained. It was found that the derived Taylor series of biharmonic Poisson integral for the upper half-plane contains the remainder in the integral form.
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 19, No. 3, pp. 434–443, July–September, 2022.
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Shutovskyi, A.M., Sakhnyuk, V.Y. Taylor Series of Biharmonic Poisson Integral for Upper Half-Plane. J Math Sci 268, 239–246 (2022). https://doi.org/10.1007/s10958-022-06195-y
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DOI: https://doi.org/10.1007/s10958-022-06195-y