Volume 9, 2003, Number 1

Volume 9 ▶ Number 1 ▷ Number 2Number 3Number 4

Generalized Bernoulli polynomials & Jackson’s calculus of sequences
Original research paper. Pages 1–6
A. G. Shannon
Full paper (PDF, 168 Kb) | Abstract

This paper considers generalized Bernoulli and exponential functions in the context of factorials formed from the elements of divisibility sequences as in the calculus of sequences of Jackson and Ward. The results for the ordinary integers readily follow. Suggestions for further relevant research with commutative diagrams are included.

Continued fraction representations for theta functions
Original research paper. Pages 7–12
C. Adiga, T. Kim, D.-W. Park, Y. S. Ro and L.-C. Jang
Full paper (PDF, 177 Kb) | Abstract

In this paper we establish continued fraction representations for theta functions, which are similar to q-continued fractions for certain q-products recorded by Ramanujan in the unorganized portions of his notebooks.

Abstract lambda polynomials and their convolutions
Original research paper. Pages 13–27
A. F. Horadam
Full paper (PDF, 494 Kb) Abstract

In the beginning we have unity, 1, and two different entities a, bx (a, b integers ≠ 1) generating a triangular algebraic “genealogical tree” in Figure 1. This pattern is called the Abstract Lambda Polynomial Triangle.

Remark on n!
Original research paper. Page 28
Krassimir T. Atanassov
Full paper (PDF, 39 Kb)

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