P. L. Robinson

activity

20122021

most citedProjective Space: Lines and Duality

3 citations · 22 across the 56 of their papers we have counts for

collaborators

56 papers

math.CV2021

The Berndt-Bhargava-Garvan Transfer Principle for signature three

P. L. Robinson

We offer a new proof for the Berndt-Bhargava-Garvan Transfer Principle that connects the signature-three elliptic theory of Ramanujan to the classical elliptic theory.

math.NT2021

Modular transformations and the elliptic functions of Shen

P. L. Robinson

We employ Weierstrassian modular transformations to compute fundamental periods for the elliptic functions $dn_{2}$ and $dn_{3}$ of Shen.

math.CA2021★ 1 cited

A root elliptic function in signature four

P. L. Robinson

We present a new approach to elliptic functions in signature four, offering a fresh perspective on work of Li-Chien Shen.

math.CV2021

Elliptic functions in signature four

P. L. Robinson

We explore the relationships between two elliptic functions constructed by Shen in the signature four Ramanujan theory.

math.CV2021

On Weierstrass $℘$ in signature 3

P. L. Robinson

In his work on the Ramanujan theory of elliptic functions to alternative bases, Shen constructed two different elliptic functions in signature three; we determine the precise relat…

math.CV2020

Hypergeometric identities in elliptic signature six

P. L. Robinson

Within the Ramanujan theories of elliptic functions, Li-Chien Shen constructed natural elliptic functions in signature three and signature four. When applied in signature six, the…

math.CV2020

The elliptic function $dn_{2}$ of Shen

P. L. Robinson

We analyze the elliptic function $dn_{2}$ introduced by Li-Chien Shen, contributing to the Ramanujan theory of elliptic functions in signature four.

math.CV2020

The elliptic function $dn_{3}$ of Shen

P. L. Robinson

We analyze the elliptic function $dn_{3}$ introduced by Li-Chien Shen, contributing to the Ramanujan theory of elliptic functions in signature three. A famous hypergeometric id…

math.CA2020

Elliptic functions from hypergeometric integrals

P. L. Robinson

As a contribution to the Ramanujan theory of elliptic functions to alternative bases, Li-Chien Shen has shown how analogues of the Jacobian elliptic functions may be derived from i…

math.CV2020

Nonelliptic functions from $F (\frac{1}{6}, \frac{5}{6}; \frac{1}{2}; ∙)$

P. L. Robinson

As contributions to the Ramanujan theory of elliptic functions to alternative bases, Li-Chien Shen has developed families of elliptic functions from the hypergeometric functions $F…

math.FA2019

Closed graphs and open maps

P. L. Robinson

We offer a new perspective on the closed graph theorem and the open mapping theorem for separated barrelled spaces and fully complete spaces.

math.FA2019

The closed graph theorem is the open mapping theorem

R. S. Monahan, P. L. Robinson

We extend the closed graph theorem and the open mapping theorem to a context in which a natural duality interchanges their extensions.

math.GM2019

Elliptic functions and flotation

P. L. Robinson

A paraboloid or a cone of density $ρ$ with vertical axis is released from rest into a liquid of density $ρ_{0}$ . We determine the critical value of the ratio $ρ_{0} / ρ$ for subsequent f…

math.CV2019

Elliptic functions from $F (\frac{1}{4}, \frac{3}{4}; \frac{1}{2}; ∙)$

P. L. Robinson

We reconsider the elliptic functions that are generated from the hypergeometric function $F (\frac{1}{4}, \frac{3}{4}; \frac{1}{2}; ∙)$ by Li-Chien Shen, presenting fresh…

math.CV2019

Elliptic functions from $F (\frac{1}{3}, \frac{2}{3}; \frac{1}{2}; ∙)$

P. L. Robinson

Li-Chien Shen developed a family of elliptic functions from the hypergeometric function $_{2} F_{1} (\frac{1}{3}, \frac{2}{3}; \frac{1}{2}; ∙)$ . We comment on this development, o…

math.CA2019

Higher Trigonometry: A Class Of Nonlinear Systems

P. L. Robinson

We study the initial value problem ' $s^{'} = c^{p - 1}, c^{'} = - s^{p - 1}; s (0) = 0, c (0) = 1$ ' (both as a real system and as a complex system) for each integer $p > 2$ ,…

math.CV2019★ 2 cited

Meromorphic functions in a first-order system

P. L. Robinson

We consider the differential equations $s^{'} = c^{5}$ and $c^{'} = - s^{5}$ with initial conditions $s (0) = 0$ and $c (0) = 1$ . We show that $s^{2} c^{2}$ extends to the reciprocal of the Weiers…

math.CV2019★ 2 cited

The Elliptic Functions in a First-Order System

P. L. Robinson

We investigate the first-order system ` $s^{'} = c^{3}, c^{'} = - s^{3}; s (0) = 0, c (0) = 1$ '. Its solutions have the property that $s c$ , $s^{2}$ and $c^{2}$ extend to simply-pol…

math.CV2019

The Lemniscatic Functions

P. L. Robinson

We develop the theory of the lemniscatic functions sl and cl from their definition as solutions to an initial value problem.

math.CV2019★ 1 cited

The Dixonian elliptic functions

P. L. Robinson

We offer a careful development of the Dixonian elliptic functions with parameter $α = 0$ from the initial value problem of which they are solutions.

math.CA2018

Bessel function asymptotics: a relation due to Lommel

P. L. Robinson

We show that the Bessel function asymptotic relation $J_{ν}^{2} (z) + J_{ν + 1}^{2} (z) \sim 2/ (π z)$ of Lommel is valid when $z$ is real but can fail otherwise.

math.FA2018★ 2 cited

Julia operators and Halmos dilations

P. L. Robinson

We offer a simple direct proof of the unitarity of the Julia operator associated to a contraction $A$ , from which follow the intertwining identity $(I - A A^*)^{1/2} A = A (I - A^*…

math.CA2017

Conservative inclusion of Nörlund methods

P. L. Robinson

We offer practical necessary and sufficient conditions in order that every sequence convergent relative to the Nörlund summation method $(N, p)$ be convergent relative to the Nörlu…

math.CA2017

Marcel Riesz on Nörlund Means

P. L. Robinson

We note that the necessary and sufficient conditions established by Marcel Riesz for the inclusion of regular Nörlund summation methods are in fact applicable quite generally.

The Berndt-Bhargava-Garvan Transfer Principle for signature three

Modular transformations and the elliptic functions of Shen

A root elliptic function in signature four

Elliptic functions in signature four

On Weierstrass ℘ in signature 3

Hypergeometric identities in elliptic signature six

The elliptic function dn2​ of Shen

The elliptic function dn3​ of Shen

Elliptic functions from hypergeometric integrals

Nonelliptic functions from F(61​,65​;21​;∙)

Closed graphs and open maps

The closed graph theorem is the open mapping theorem

Elliptic functions and flotation

Elliptic functions from F(41​,43​;21​;∙)

Elliptic functions from F(31​,32​;21​;∙)

Higher Trigonometry: A Class Of Nonlinear Systems

Meromorphic functions in a first-order system

The Elliptic Functions in a First-Order System

The Lemniscatic Functions

The Dixonian elliptic functions

Bessel function asymptotics: a relation due to Lommel

Julia operators and Halmos dilations

Conservative inclusion of Nörlund methods

Marcel Riesz on Nörlund Means

On Weierstrass $℘$ in signature 3

The elliptic function $dn_{2}$ of Shen

The elliptic function $dn_{3}$ of Shen

Nonelliptic functions from $F (\frac{1}{6}, \frac{5}{6}; \frac{1}{2}; ∙)$

Elliptic functions from $F (\frac{1}{4}, \frac{3}{4}; \frac{1}{2}; ∙)$

Elliptic functions from $F (\frac{1}{3}, \frac{2}{3}; \frac{1}{2}; ∙)$