Larcombe, Peter J.; Riese, Axel; Zimmermann, Burkhard Computer proofs of matrix product identities. (English) Zbl 1087.15017 J. Algebra Appl. 3, No. 1, 105-109 (2004). A straightforward but useful method for computing indefinite rational matrix products is presented. The method is used to prove the identity \[ \int_0^{\infty }e^{(ir-m)x} (1-e^{-x})^n dx=\sum_{j=0}^n (-1)^j {n\choose j} \frac{m+j}{(m+j)^2 +r^2} +i\sum_{j=0}^n (-1)^j {n\choose j} \frac{r}{(m+j)^2+r^2}. \] Reviewer: Nicholas Karampetakis (Thessaloniki) MSC: 15A24 Matrix equations and identities 33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) 68W30 Symbolic computation and algebraic computation Keywords:computer algebra; definite integration; recurrence relations; computer proof; indefinite rational matrix products PDFBibTeX XMLCite \textit{P. J. Larcombe} et al., J. Algebra Appl. 3, No. 1, 105--109 (2004; Zbl 1087.15017) Full Text: DOI References: [1] DOI: 10.1016/0304-3975(95)00173-5 · Zbl 0868.34004 · doi:10.1016/0304-3975(95)00173-5 [2] DOI: 10.1006/jsco.1995.1071 · Zbl 0851.68052 · doi:10.1006/jsco.1995.1071 [3] DOI: 10.1016/S0195-6698(80)80051-5 · Zbl 0445.05012 · doi:10.1016/S0195-6698(80)80051-5 [4] DOI: 10.1016/0012-365X(90)90120-7 · Zbl 0701.05001 · doi:10.1016/0012-365X(90)90120-7 [5] DOI: 10.1016/S0747-7171(08)80044-2 · Zbl 0738.33002 · doi:10.1016/S0747-7171(08)80044-2 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.