Kumar, D.; Srivastava, G. S.; Kasana, H. S. Approximation of entire harmonic functions in \(R^ 3\) having index-pair \((p,q)\). (English) Zbl 0756.41024 Math., Rev. Anal. Numér. Théor. Approximation, Anal. Numér. Théor. Approximation 20, No. 1-2, 47-57 (1991). Summary: The authors define approximation error for harmonic functions in \(H_ R\), \(0<R<\infty\), the class of all harmonic functions \(H\) in \(R^ 3\), that are regular in the open ball \(D_ R\) of radius \(R\) centered at the origin and are continuous on the closure \(\overline D_ R\) of \(D_ R\); norm being the sup. norm. Necessary and sufficient conditions, in terms of the rate of decay of the approximation error \(E_ n(H,R)\), such that \(H\in H_ R\) has analytic continuation as an entire harmonic function having \((p,q)\)-order \(\rho\) and lower \((p,q)\)-order \(\lambda\), are obtained. MSC: 41A25 Rate of convergence, degree of approximation 40C10 Integral methods for summability 41A30 Approximation by other special function classes 30E05 Moment problems and interpolation problems in the complex plane Keywords:harmonic functions; rate of decay of the approximation error PDFBibTeX XMLCite \textit{D. Kumar} et al., Math. Rev. Anal. Numér. Théor. Approximation, Anal. Numér. Théor. Approximation 20, No. 1--2, 47--57 (1991; Zbl 0756.41024)