7 citations · 14 across the 13 of their papers we have counts for
13 papers
Some integrals which are not in table 129 of Bierens de Haan
Enno Diekema
In the standard work of Bierens de Haan about integrals we look at table 129. This table lists a number of integrals of a certain kind. In this paper the table is expanded with a n…
Exact formulas for the fourth and fifth cumulant of the Rosenblatt distribution
Enno Diekema
In an earlier version of this paper \cite{6} a formula for the 4th cumulant of the Rosenblatt distribution was derived. In this paper formulas for the 3rd, 4th and 5th cumulant are…
On the linear (in)dependence of sequences of derivatives of the functions and
Jozef Fecenko, Enno Diekema
The main goal of the paper is to prove that the sequence of functions , where is or are linearly independent. Or mo…
Combinatorial identities and hypergeometric series
Enno Diekema
This paper describes a method to find a connection between combinatorial identities and hypergeometric series with a number of examples. Combinatorial identities can often be writt…
Some definite integrals involving Jacobi polynomials
Enno Diekema
Szmytkowski derived a certain integral with Gegenbauer polynomials. A natural generalization is to derive lookalike integrals with Jacobi polynomials. Six methods are treated to de…
The Catalan-Qi number of the second kind and a related integral
Enno Diekema
Li et al. give an integral formula for the Catalan-Qi number of the second kind. They show that this integral can be written as a summation with double factorials. In this paper th…
The orthogonal Shmaliy polynomials are Hahn polynomials
Enno Diekema
Morales-Mendoza et al. present in 2013 a new class of discrete orthogonal polynomials. They use these polynomials to design an unbiased FIR filter. In their paper they make the sta…
An extension of the orthogonal derivative with adjustable precision
Enno Diekema
The orthogonal derivative is defined as a limit of an integral whose kernel contains an orthogonal polynomial with its measure. When in practice no limit is taken, it means that th…
The two-dimensional fractional orthogonal derivative
Enno Diekema
This paper is an edited and shortened version of Chapter 6 from the thesis of the author. First the one dimensional orthogonal derivative will be extended to the two-dimensional ca…
A correlation function for the classical orthogonal polynomials
Enno Diekema
A correlation function of the classical orthogonal polynomials is defined and determined. The correlation function obeys a second order difference equation in two variables. The co…
Integral representations for Horn's function and Olsson's function
Enno Diekema, Tom H. Koornwinder
We derive some Euler type double integral representations for hypergeometric functions in two variables. In the first part of this paper we deal with Horn's function, in the…
The fractional orthogonal derivative
E. Diekema
This paper builds on the notion of the so-called orthogonal derivative, where an n-th order derivative is approximated by an integral involving an orthogonal polynomial of degree n…
Generalizations of an integral for Legendre polynomials by Persson and Strang
Enno Diekema, Tom H. Koornwinder
Persson and Strang (2003) evaluated the integral over [-1,1] of a squared odd degree Legendre polynomial divided by x^2 as being equal to 2. We consider a similar integral for orth…