Expansion Of Harmonic Functions Research Articles

On the Flow About a Spheroid Near a Plane Wall

The problem of incompressible potential flow about a prolate spheroid in axial motion parallel to a plane wall is considered and a solution free of any approximations, although not in closed form, is obtained. The added-mass coefficient for this motion is evaluated and the results are compared with an existing approximate solution. The expansion of harmonic functions of the form exp(αx +βy +γz) in a series of spheroidal harmonics, needed in the solution of the preceding problem and useful in general in the analysis of problems in potential theory in which spheroidal boundaries appear, is obtained.

On the Expansion of Harmonic Functions in Series of Harmonic Polynomials Belonging to a Simply Connected Region

On the Expansion of Harmonic Functions in Series of Harmonic Polynomials Belonging to a Simply Connected Region

On the Expansion of Harmonic Functions in Terms of Normal-Orthogonal Harmonic Polynomials

Consiaer a closed, rectifiable Jordan curve, C, lying in the (x y)-plane, possessing continuous curvature, and of length u-. Let f(x,y) be a function which is harmonic inside C and continuous in the closed region 0 consisting of C and its interior. The present paper is concerned with the development of f(x,y) in terms of a set of harmonic polynomials Pm(x,y), which are linear combinations of the functions 1, x, y, x2 y2, Xyy . Let

Note on the Expansion of Harmonic Functions in the Neighborhood of Isolated Singular Points

Note on the Expansion of Harmonic Functions in the Neighborhood of Isolated Singular Points

On the Expansion of Harmonic Functions in Terms of Harmonic Polynomials

On the Expansion of Harmonic Functions in Terms of Harmonic Polynomials