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Obtuse matrix of arithmetic table
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In the work we generate arithmetic matrix $P^{(c,b,a)}$ of $(cx^2+bx+a)^n$from a Pascal matrix $P^{(1,1)}$. We extend an identity $P^{(1,1)} O^{(1,1)} =P^{(1,1,1)}$ with an obtuse matrix $O^{(1,1)}$to $k$ degree polynomials. For the purpose we study ${P^{(1,1)}}^k O^{(1,1)}$and find generating polynomials of ${O^{(1,1)}}^k$.
Abstract
In the work we generate arithmetic matrix $P^{(c,b,a)}$ of $(cx^2+bx+a)^n$from a Pascal matrix $P^{(1,1)}$. We extend an identity $P^{(1,1)} O^{(1,1)} =P^{(1,1,1)}$ with an obtuse matrix $O^{(1,1)}$to $k$ degree polynomials. For the purpose we study ${P^{(1,1)}}^k O^{(1,1)}$and find generating polynomials of ${O^{(1,1)}}^k$.
참고문헌 (6)
- L. Aceto, "The matrices of pascal and other greats", Amer. Math. Monthly, 108, pp.232~245 (2001)
- E. Horowitz, "The computations of powers of symbolic polynomials", SIAM J. Comput, 4, pp.201~208 (1975)
- J. Jo, "Arithmetic matrix of quadratic polynomial with negative exponent by Pascal matrix", J. of Alg. and Appl. Math, 17, pp.67~90 (2019)
- D. Loeb, "A generalization of the binomial coefficients", Discrete Math, 105, pp.143~156 (1992)
- "Entry A122888" (2024)[URL]
- C. Ponder, "Parallel multiplication and powering of polynomials", J. Symbolic Computation, 11, pp.307~320 (1991)
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