An integral representation is provided for the parabolic cylinder function product $D_{\mu}(x)D_{\mu}(-y)$ where $Re\,\mu<0$ and $x>y$ are unrelated. A few simple consequences are given in the form of hyperbolic integrals and a sum rule.
Integral representation of functions on the circle
Integral Representations of Ultraspherical Polynomials II
Two forms of the integral representations of the Mittag-Leffler function
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