Factorizations related to the reciprocal Pascal matrix

Authors: HELMUT PRODINGER

Abstract: The reciprocal Pascal matrix has entries $\binom{i+j}{j}^{-1}$. Explicit formul$\ae{}$ for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, $q$-analogues are also presented.

Keywords: Pascal matrix, LU-decomposition, $q$-analogue, Zeilberger's algorithm

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