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On the probability density function of the Hartman- Watson distribution

The Hartman-Watson distribution arises in many areas of applied probability. But its probability density function is difficult to compute. Recently, [13] gave the first two terms of its asymptotic expansion. Here, we derive the probability density function and a full asymptotic expansion in computable forms.

Computable series representation ; Hartman-Watson distribution ; Laplace-Mellin transform ; Parabolic cylinder function

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