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Bulletin of the London Mathematical Society, 1971
Lajos Takacs, John Riordan
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Lajos Takacs, John Riordan
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Some Combinatorial Identities of Bernstein
SIAM Journal on Mathematical Analysis, 1978For g a rational integer such that $\Delta = 4g^3 + 27$ is square-free, let w denote the real root of $u^3 + gu - 1 = 0$ and put $w^n = r_n + s_n w + t_n w^2 $, $w^{ - n} = x_n + y_n w + z_n w^2 $, $n \geqq 0$. Making use of the theory of units in an algebraic number field, Bernstein obtained quadratic relations involving the $r_n $ and $x_n $ as well ...
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Divided Differences and Combinatorial Identities
Studies in Applied Mathematics, 1991We present an algebraic theory of divided differences which includes confluent differences, interpolation formulas, Liebniz's rule, the chain rule, and Lagrange inversion. Our approach uses only basic linear algebra. We also show that the general results about divided differences yield interesting combinatorial identities when we consider some suitable
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Inversion Techniques and Combinatorial Identities
1994The purpose of this article is to emphasize the usefulness of inverse relations in order to derive (possibly) new identities from known ones. This method was made popular by \textit{J. Riordan} [``Combinatorial identities'' (1968; Zbl 0194.005)]. Suppose tht \((M_{nk})_{n,k\geq 0}\) and \((M^{-1}_{nk})_{n,k\geq 0}\) are (infinite-dimensional) lower ...
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