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Integrals and series. Vol. 4: Direct Laplace transforms. (English) Zbl 0786.44003
New York: Gordon and Breach Science Publishers. xx, 619 p. \$ 170.00 (1992).

This book comprises a very extensive list of direct Laplace transforms, including many published for the first time. The tabulation follows the conventional “original function in the left-, transformation in the right-hand columns”, whilst the required formulae can be found from a detailed contents list at the front of the book.

Most of the functions associated with the theory of operational calculus are represented, including the theta functions, but not the Jacobian elliptic functions, although a reference is given for these latter doubly periodic functions in a comprehensive bibliography at the end of the book.

Of passing interest is the way periodicity can be imposed on representative function segments by replacing the argument with its entier, i.e. for arbitrary $f\left(t\right)$, $f\left(\left[t\right]\right)$ is periodic. This idea figures quite prominently throughout the tables.

Finally, an appendix summarises the properties and applications of Laplace transforms, and there is a particularly edifying bit on the solution of differential and integral equations by the method of Laplace transforms.

##### MSC:
 44A10 Laplace transform 44-00 Reference works (integral transforms) 44A35 Convolution (integral transforms) 00A22 Formularies 44A20 Integral transforms of special functions 33-00 Reference works (special functions)