q-Newton Binomial: From Euler To Gauss
نویسنده
چکیده
X iv :m at h/ 00 04 18 7v 1 [ m at h. H O ] 1 A pr 2 00 0 Journal of Nonlinear Mathematical Physics 2000, V.7, N 2, 244–262. (Re)-Examining the Past q-Newton Binomial: From Euler To Gauss Boris A. KUPERSHMIDT The University of Tennessee Space Institute, Tullahoma, TN 37388, USA E-mail: [email protected] Received March 6, 2000; Accepted April 7, 2000 Abstract A counter-intuitive result of Gauss (formulae (1.6), (1.7) below) is made less mysterious by virtue of being generalized through the introduction of an additional parameter. 1 A formula of Gauss revisited Consider the Newton binomial for a positive integer N : (1− x) = N
منابع مشابه
More on Combinatorial Interpretation of Fibonomial Coefficients
A classical-like combinatorial interpretation of the Fibonomial coefficients is proposed following [1,2]. It is considered to be in the spirit classicalcombinatorial interpretation like binomial Newton and Gauss q-binomial coefficients or Stirling number of both kinds are. (See ref. [3,4] and refs. given therein). It also concerns choices. Choices of specific sub-posets from a non-tree poset sp...
متن کاملAN ALGEBRAIC INTERPRETATION OF THE q-BINOMIAL COEFFICIENTS
Gaussian numbers, also called Gaussian polynomials or q-binomial coefficients are the q-analogs of common binomial coefficients. First introduced by Euler these polynomials have played an important role in many different branches of mathematics. Sylvester discovered the unimodality of their coefficients, using invariant theory. Gauss recognized the connection of the coefficients to proper integ...
متن کاملPreconditioners for Linearized Discrete Compressible Euler Equations
We consider a Newton-Krylov approach for discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is essential for obtaining an efficient solver in such an approach. In this paper we compare point-block-Gauss-Seidel, point-block-ILU and point-block-SPAI preconditioners. It turns out that the SPAI method is not satisfactory for our problem class. The point-bl...
متن کاملCombinatorial interpretation of the recurrence relation for fibonomial coefficients
A classical-like combinatorial interpretation of the Fibonomial coefficients is provided following [1,2]. An adequate combinatorial interpretation of recurrence satisfied by Fibonomial coefficients is also proposed. It is considered to be in the spirit classicalcombinatorial interpretation like binomial Newton and Gauss q-binomial coefficients or Stirling number of both kinds are. (See ref. [3,...
متن کاملNumbering Techniques for Preconditioners in Iterative Solvers for Compressible Flows
We consider Newton-Krylov methods for solving discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is crucial for the efficiency of the solver. In this paper we consider a point-block Gauss-Seidel method as preconditioner. We describe and compare renumbering strategies that aim at improving the quality of this preconditioner. A variant of reordering meth...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000