Abstract
In electromagnetics and acoustics, difficulties are encountered in evaluations of integrals containing the free-space scalar Green's Function <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$G(\mathbf{r},{{\bf r^{\prime}}})$</tex-math></inline-formula> . So-called far-field approximations have long been used for obtaining approximate solutions. We have developed new approximations by using the Taylor Product Theorem that are equally simple but far more accurate as demonstrated by numerical examples. Additionally, we have developed error estimates.
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