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 math.CVShow all

15 papers · 1 filter

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.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.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.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.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.CV2016

Neville's primitive elliptic functions: the case $g_{3} = 0$

P. L. Robinson

The vanishing of the invariant $g_{3}$ attached to a lattice $Λ$ singles out a midpoint lattice and yields a square-root of the associated Weierstrass function $℘_{Λ}$ .

math.CV2016

Remarks on trigonometric functions after Eisenstein

P. L. Robinson

We modify the Whittaker-Watson account of the Eisenstein approach to the trigonometric functions, basing these functions independently on the Eisenstein function $ε_{2}$ .

The Berndt-Bhargava-Garvan Transfer Principle for signature three

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

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

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

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

Meromorphic functions in a first-order system

The Elliptic Functions in a First-Order System

The Lemniscatic Functions

The Dixonian elliptic functions

Neville's primitive elliptic functions: the case g3​=0

Remarks on trigonometric functions after Eisenstein

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

Neville's primitive elliptic functions: the case $g_{3} = 0$