During the last decade, the large scale digital computer has become available to almost all scientists. The speed and accuracy of such machines has led some people to use mathematical methods that are not always appropriate. The primary purpose of this paper is to discuss some numerical methods for the improvement of the convergence of series encountered in acoustical theories. This paper is restricted to general comments and a discussion of one special case, namely the mutual mechanical impedance between circular pistons in an infinite plane rigid baffle, which has been represented by Pritchard as a double or single series of Bessel function products. If the separation of the two pistons is large as compared with the diameter of the pistons, the series can be represented to sufficient accuracy by its partial sum of a very few terms. On the other hand, if the separation is only slightly greater than the diameter, a large number of terms must be included in the partial sum. Methods for reducing the numerical computations and/or improving the accuracy of results have been studied. An integral method has been used with excellent success.
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