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Computer proofs of matrix product identities. (English) Zbl 1087.15017

A straightforward but useful method for computing indefinite rational matrix products is presented. The method is used to prove the identity \[ \int_0^{\infty }e^{(ir-m)x} (1-e^{-x})^n dx=\sum_{j=0}^n (-1)^j {n\choose j} \frac{m+j}{(m+j)^2 +r^2} +i\sum_{j=0}^n (-1)^j {n\choose j} \frac{r}{(m+j)^2+r^2}. \]

MSC:

15A24 Matrix equations and identities
33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)
68W30 Symbolic computation and algebraic computation
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[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
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