Abstract
A systematic way of ascribing values to integrals which diverge at infinity is described. For integrals with algebraic or logarithmic behaviour it is akin to Hadamard's finite part for integrands which have singularities at finite points. The power of the method is illustrated by examples of particular integrals and the convolution of distributions which are beyond the range of standard theory. Both one-dimensional and multi-dimensional integrals are included. The theory also enables the definition of products of distributions which are considered normally to be too singular for multiplication.
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