20 citations · 60 across the 20 of their papers we have counts for
20 papers
The q-Binomial Coefficient for Negative Arguments and Some q-Binomial Summation Identities
M. J. Kronenburg
Using a property of the q-shifted factorial, an identity for q-binomial coefficients is proved, which is used to derive the formulas for the q-binomial coefficient for negative arg…
Computation of , the Number of Integer Partitions of into Exactly Parts
M. J. Kronenburg
Two algorithms for computing , the number of integer partitions of into exactly parts, are described, and using a combination of these two algorithms, the resulting…
Distinct Partitions and Some q-Binomial Summation Identities
M. J. Kronenburg
The partition functions , the number of integer partitions of into exactly parts with each part at most , and , the number of integer partitons of $n…
Computation of q-Binomial Coefficients with the Integer Partition Function
M. J. Kronenburg
Using , the number of integer partitions of into exactly parts, which was the subject of an earlier paper, , the number of integer partitions of into…
Some Generalized Multi-sum Chu-Vandermonde Identities
M. J. Kronenburg
Some generalized multi-sum Chu-Vandermonde identities are presented and proved, generalizing some known multi-sum Chu-Vandermonde identities from literature and adding some quadrat…
Some Weighted Generalized Fibonacci Number Summation Identities, Part 2
M. J. Kronenburg
In part 1 of this paper some linear weighted generalized Fibonacci number summation identities were derived using the fact that the Fibonacci number is the residue of a rational fu…
Higher Derivatives of the Tangent and Inverse Tangent Functions and Chebyshev Polynomials
M. J. Kronenburg
The higher derivatives of the tangent and hyperbolic tangent functions are determined. Formulas for the higher derivatives of the inverse tangent and inverse hyperbolic tangent fun…
Some Weighted Generalized Fibonacci Number Summation Identities, Part 1
M. J. Kronenburg
The Fibonacci number is the residue of a rational function, from which follows that Fibonacci number summation identities can be derived with the integral representation method, a…
Four New Generalized Fibonacci Number Summation Identities
M. J. Kronenburg
Two new generalized Fibonacci number summation identities are stated and proved, and two other new generalized Fibonacci number summation identities are derived from these, of whic…
Some Variations of Two Combinatorial Identities
M. J. Kronenburg
Given two combinatorial identities proved earlier, a new set of variations of these combinatorial identities is listed and proved with the integral representation method. Some iden…
A Generalization of the Chu-Vandermonde Convolution and some Harmonic Number Identities
M. J. Kronenburg
A generalization of the Chu-Vandermonde convolution is presented and proved with the integral representation method. This identity can be transformed into another identity, which h…
Some Identities involving Two Sets of Basis Vectors and the Metric and Mixed Matrices
M. J. Kronenburg
Given two sets of basis vectors in n-dimensional space, there exists a relation between their lengths and mutual angles, expressed as relations between the two metric matrices and…
Toom-Cook Multiplication: Some Theoretical and Practical Aspects
M. J. Kronenburg
Toom-Cook multiprecision multiplication is a well-known multiprecision multiplication method, which can make use of multiprocessor systems. In this paper the Toom-Cook complexity i…
A Method for Fast Diagonalization of a 2x2 or 3x3 Real Symmetric Matrix
M. J. Kronenburg
A method is presented for fast diagonalization of a 2x2 or 3x3 real symmetric matrix, that is determination of its eigenvalues and eigenvectors. The Euler angles of the eigenvector…
Some Harmonic Number Identities involving certain Reciprocals
Maarten Kronenburg
Some finite series of harmonic numbers involving certain reciprocals are evaluated. Products of such reciprocals are expanded in a sum of the individual reciprocals, leading to a c…
On Two Types of Harmonic Number Identities
Maarten Kronenburg
Two types of finite series of products of harmonic numbers involving nonnegative integer powers are evaluated, also yielding two other important harmonic number identities. The rec…
The Binomial Coefficient for Negative Arguments
M. J. Kronenburg
The definition of the binomial coefficient in terms of gamma functions also allows non-integer arguments. For nonnegative integer arguments the gamma functions reduce to factorials…
Some Combinatorial Identities from the Random Walk
M. J. Kronenburg
Eight combinatorial identities are listed and proved by counting paths in the one-dimensional random walk. Four of these identities are assumed to be new.
Some Generalized Harmonic Number Identities
Maarten Kronenburg
Summation by parts is used to find the sum of a finite series of generalized harmonic numbers involving a specific polynomial or rational function. The Euler-Maclaurin formula for…
Some Combinatorial Identities some of which involving Harmonic Numbers
M. J. Kronenburg
A product difference equation is proved and used for derivation by elementary methods of four combinatorial identities, eight combinatorial identities involving generalized harmoni…