A Generalization of Two q-Identities of Andrews
โ Scribed by Kuo-Jye Chen; H.M. Srivastava
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 87 KB
- Volume
- 95
- Category
- Article
- ISSN
- 0097-3165
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โฆ Synopsis
The main object of the present paper is to give a unification (and generalization) of two interesting q-identities which were proven recently by George E. Andrews. Some related results involving the Fibonacci numbers are also considered.
2001
๐ SIMILAR VOLUMES
n-dimensional lattice paths which do not touch the hyperplanes xi-xi + I = -1, i = 1,2, , n -1, and x,-x1 = -1 -K arc enumerated by certain statistics, one of which is MacMahon's major index, the others being variations of it. By a reflection-like proof, a formula involving determinants is obtained.
The ordinary binomial theorem may be expressed in the statement that the polynomials x" are of binomial type. Several generalizations of the binomial theorem can be stated in this form. A particularly nice one, essentially due to Rothe, is that the polynomials a,(x; h,w)= ## x(x+h+nw)(x+2h+nw)...(x