1 citations · 1 across the 8 of their papers we have counts for
8 papers
On a specific family of orthogonal polynomials of Bernstein-Szegö type
Martin Nicholson
We study a class of weight functions on , which are special cases of the general weights studied by Bernstein and Szegö, as well as their extentions to the interval $[-a,1]…
Self-reciprocal functions and double Mordell integrals
Martin Nicholson
The theory of self-reciprocal functions is applied to the study Mordell type integrals. We find two particular eigenfunctions of the double cosine Fourier transform and then use th…
A sequence of elementary integrals related to integrals studied by Glaisher that contain trigonometric and hyperbolic functions
Martin Nicholson
We generalize several integrals studied by Glaisher. These ideas are then applied to obtain an analog of an integral due to Ismail and Valent.
On certain finite and infinite sums of inverse tangents
Martin Nicholson
An identity is proved connecting two finite sums of inverse tangents. This identity is discretized version of Jacobi's imaginary transformation for the modular angle from the theor…
Quadratic Transformations of Hypergeometric Function and Series with Harmonic Numbers
Martin Nicholson
In this brief note, we show how to apply Kummer's and other quadratic transformation formulas for Gauss' and generalized hypergeometric functions in order to obtain transformation…
Integrals containing the infinite product
Martin Nicholson
We study several integrals that contain the infinite product in the denominator of their integrand. T…
Two-dimensional Fourier transformations and double Mordell integrals
Martin Nicholson
Fourier transformations of several functions of one and two variables are evaluated and then used to derive some integral and series identities. It is shown that certain double Mor…
Finite and infinite product transformations
Martin Nicholson
Several infinite products are studied that satisfy the transformation relation of the type . For certain values of the parameters these infinite products reduce to mod…