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Experimental evaluation of user performance in a pursuit tracking task with multimodal feedback. (English) Zbl 1150.11345

For each \(k\geq1\) there are integers \(u_k\), \(v_k\), such that \[ \sum_{i=0}^{n-1}\varepsilon^ii!(i^k+u_k)=v_k+\varepsilon^{n-1}n!A_{k-1}(n), \] where \(\varepsilon=\pm1\) and \(A_{k-1}\) is a polynomial of degree \(k-1\). New equivalents of the Kurepa hypothesis [Đ. Kurepa, Math. Balk. 1, 147–153 (1971; Zbl 0224.10009)] on the left factorial are found.

MSC:

11B65 Binomial coefficients; factorials; \(q\)-identities

Citations:

Zbl 0224.10009
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