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

Showing 2019Show all

10 papers · 1 filter

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.

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

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

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