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Laplace approximation for Bessel functions of matrix argument. (English) Zbl 1027.65033
The authors present Laplace approximations to Bessel functions of matrix argument and to the confluent type II matrix argument hypergeometric function. A collection of results concerning the theoretical properties of the various Laplace approximations is proved. In particular, it is shown that suitably calibrated versions of the approximations inherit the symmetries and confluence relations satisfied by the original functions. A series of tables with results of calculations is given.

##### MSC:
 65D20 Computation of special functions, construction of tables 33C10 Bessel and Airy functions, cylinder functions, ${}_0F_1$ 33C15 Confluent hypergeometric functions, Whittaker functions, ${}_1F_1$ 33F05 Numerical approximation and evaluation of special functions
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