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Your search keyword '"*BINOMIAL theorem"' showing total 2 results
Start Over Descriptor "*BINOMIAL theorem" Topic algebra Publisher american institute of physics
2 results on '"*BINOMIAL theorem"'

1. Characterization of linear recurrences associated to rays in Pascal’s triangle.

Author

Belbachir, Hacène, Komatsu, Takao, and Szalay, László

Subjects
*PASCAL'S triangle, *BINOMIAL coefficients, *BINOMIAL theorem, *POLYNOMIALS, *ALGEBRA, *FINITE differences
Abstract

Our purpose is to describe the recurrence relations associated to the sum of diagonal elements laying along a finite ray crossing Pascal’s triangle. We also answer Horadam’s question posed in his paper entitled Chebyshev and Pell connections, Fibonacci Quart., (2005). Further, using Morgan-Voyce sequence, we establish the nice identity Fn+1-iFn = in∑k = 0n(2kn+k)(-2-i)k of Fibonacci numbers, where i = -11. Finally, connections to continued fractions, bivariate polynomials and finite differences are given. [ABSTRACT FROM AUTHOR]

Published
2010
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2. Expansion around half-integer values, binomial sums, and inverse binomial sums.

Author

Weinzierl, Stefan

Subjects
*MATHEMATICAL physics, *MATHEMATICAL functions, *ALGORITHMS, *ALGEBRA, *BINOMIAL theorem, *INVERSE functions
Abstract

I consider the expansion of transcendental functions in a small parameter around rational numbers. This includes in particular the expansion around half-integer values. I present algorithms which are suitable for an implementation within a symbolic computer algebra system. The method is an extension of the technique of nested sums. The algorithms allow in addition the evaluation of binomial sums, inverse binomial sums and generalizations thereof. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Published
2004
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