We prove that the Bernoulli numbers satisfy some special lower triangular Toeplitz systems of linear equations. One of these systems has a strong link with eleven Ramanujan's linear equations satisfied by the first eleven Bernoulli numbers.
- Bernoulli numbers
- triangular Toeplitz matrices
Di Fiore, C., Tudisco, F., & Zellini, P. (2016). Lower triangular Toeplitz-Ramanujan systems whose solution yields the Bernoulli numbers. Linear Algebra and its Applications, 496, 510-526. https://doi.org/10.1016/j.laa.2016.02.007