965 research outputs found
Note on Ward-Horadam H(x) - binomials' recurrences and related interpretations, II
We deliver here second new recurrence formula,
were array is appointed by sequence of
functions which in predominantly considered cases where chosen to be
polynomials . Secondly, we supply a review of selected related combinatorial
interpretations of generalized binomial coefficients. We then propose also a
kind of transfer of interpretation of coefficients onto
coefficients interpretations thus bringing us back to
and Donald Ervin Knuth relevant investigation decades
ago.Comment: 57 pages, 8 figure
The congruence of Wolstenholme and generalized binomial coefficients related to Lucas sequences
Using generalized binomial coefficients with respect to fundamental Lucas
sequences we establish congruences that generalize the classical congruence of
Wolstenholme and other related stronger congruences.Comment: 23 page
Some new -congruences for truncated basic hypergeometric series
We provide several new -congruences for truncated basic hypergeometric
series, mostly of arbitrary order. Our results include congruences modulo the
square or the cube of a cyclotomic polynomial, and in some instances,
parametric generalizations thereof. These are established by a variety of
techniques including polynomial argument, creative microscoping (a method
recently introduced by the first author in collaboration with Zudilin),
Andrews' multiseries generalization of the Watson transformation, and
induction. We also give a number of related conjectures including congruences
modulo the fourth power of a cyclotomic polynomial.Comment: 14 pages, more background and references adde
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