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Matrix argument K Bessel functions at half integral orguments

As a working definition I will define: $$ K_\nu^{(n)} (z) = \frac{1}{2^n}\int_{\mathcal{P}} e^{- \operatorname{tr}( y + y^{-1}) z/2} \det y^\nu d \mu(y) $$ where $\mathcal{P}$ represents the space of …
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