Zobrazeno 1 - 10
of 38
pro vyhledávání: '"Kronenburg, M. J."'
Autor:
Kronenburg, M. J.
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 arguments. The result is in agreement with an earlier paper about the nor
Externí odkaz:
http://arxiv.org/abs/2211.08256
Autor:
Kronenburg, M. J.
The partition functions $P(n,m,p)$, the number of integer partitions of $n$ into exactly $m$ parts with each part at most $p$, and $Q(n,m,p)$, the number of integer partitons of $n$ into exactly $m$ distinct parts with each part at most $p$, are rela
Externí odkaz:
http://arxiv.org/abs/2206.05062
Autor:
Kronenburg, M. J.
Using $P(n,m)$, the number of integer partitions of $n$ into exactly $m$ parts, which was the subject of an earlier paper, $P(n,m,p)$, the number of integer partitions of $n$ into exactly $m$ parts with each part at most $p$, can be computed in $O(n^
Externí odkaz:
http://arxiv.org/abs/2205.15013
Autor:
Kronenburg, M. J.
Two algorithms for computing $P(n,m)$, the number of integer partitions of $n$ into exactly $m$ parts, are described, and using a combination of these two algorithms, the resulting algorithm is $O(n^{3/2})$. The second algorithm uses a list of $P(n)$
Externí odkaz:
http://arxiv.org/abs/2205.04988
Autor:
Kronenburg, M. J.
Some generalized multi-sum Chu-Vandermonde identities are presented and proved, generalizing some known multi-sum Chu-Vandermonde identities from literature and adding some quadratic and cubic examples of these identities. Some other closely related
Externí odkaz:
http://arxiv.org/abs/2111.11864
Autor:
Kronenburg, M. J.
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 function. In this part, using the same method, some quadratic and cubic
Externí odkaz:
http://arxiv.org/abs/2106.11838
Autor:
Kronenburg, M. J.
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 functions as polynomials are stated and proved. Using another formula for
Externí odkaz:
http://arxiv.org/abs/2010.09862
Autor:
Kronenburg, M. J.
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 method also used to derive combinatorial identities. A number of weigh
Externí odkaz:
http://arxiv.org/abs/1903.01407
Autor:
Kronenburg, M. J.
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 which two special cases are already known in literature.
Externí odkaz:
http://arxiv.org/abs/1806.08335
Autor:
Kronenburg, M. J.
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 identities from literature are shown to be special cases of these new iden
Externí odkaz:
http://arxiv.org/abs/1705.05675