Sheng-liang Yang, Zhong-kui Liu, "Explicit inverse of the Pascal matrix plus one", International Journal of Mathematics and Mathematical Sciences, vol. 2006, Article ID 090901, 7 pages, 2006. https://doi.org/10.1155/IJMMS/2006/90901
Explicit inverse of the Pascal matrix plus one
This paper presents a simple approach to invert the matrix by applying the Euler polynomials and Bernoulli numbers, where is the Pascal matrix.
- L. Aceto and D. Trigiante, “The matrices of Pascal and other greats,” The American Mathematical Monthly, vol. 108, no. 3, pp. 232–245, 2001.
- R. Aggarwala and M. P. Lamoureux, “Inverting the Pascal matrix plus one,” The American Mathematical Monthly, vol. 109, no. 4, pp. 371–377, 2002.
- M. Bayat and H. Teimoori, “Pascal -eliminated functional matrix and its property,” Linear Algebra and Its Applications, vol. 308, no. 1–3, pp. 65–75, 2000.
- R. Brawer and M. Pirovino, “The linear algebra of the Pascal matrix,” Linear Algebra and Its Applications, vol. 174, pp. 13–23, 1992.
- G. S. Call and D. J. Velleman, “Pascal's matrices,” The American Mathematical Monthly, vol. 100, no. 4, pp. 372–376, 1993.
- G.-S. Cheon, “A note on the Bernoulli and Euler polynomials,” Applied Mathematics Letters, vol. 16, no. 3, pp. 365–368, 2003.
- L. Comtet, Advanced Combinatorics. The Art of Finite and Infinite Expansions, D. Reidel, Dordrecht, 1974.
- K. H. Rosen, J. G. Michaels, J. L. Gross, J. W. Grossman, and D. R. Shier, Eds., Handbook of Discrete and Combinatorial Mathematics, CRC Press, Florida, 2000.
- H. M. Srivastava and Á. Pintér, “Remarks on some relationships between the Bernoulli and Euler polynomials,” Applied Mathematics Letters, vol. 17, no. 4, pp. 375–380, 2004.
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