scholarly journals The sigma function for trigonal cyclic curves

2018 ◽  
Vol 109 (2) ◽  
pp. 423-447
Author(s):  
Jiryo Komeda ◽  
Shigeki Matsutani ◽  
Emma Previato
Keyword(s):  
Sigma Function

scholarly journals A Hirota bilinear equation for Painlevé transcendents PIV, PII and PI

2018 ◽  
Vol 07 (04) ◽  
pp. 1840001
Author(s):  
A. N. W. Hone ◽  
F. Zullo
Keyword(s):  
Taylor Series ◽  
Taylor Expansion ◽  
Tau Function ◽  
Tau Functions ◽  
Sigma Function ◽  
Special Cases ◽  
Hirota Bilinear Equation ◽  
Order Four ◽  
Hirota Bilinear ◽  
Bilinear Equation

We present some observations on the tau-function for the fourth Painlevé equation. By considering a Hirota bilinear equation of order four for this tau-function, we describe the general form of the Taylor expansion around an arbitrary movable zero. The corresponding Taylor series for the tau-functions of the first and second Painlevé equations, as well as that for the Weierstrass sigma function, arise naturally as special cases, by setting certain parameters to zero.

scholarly journals Sato Grassmannian and Degenerate Sigma Function

2020 ◽  
Vol 374 (2) ◽  
pp. 627-660 ◽  
Author(s):  
Julia Bernatska ◽  
Victor Enolski ◽  
Atsushi Nakayashiki
Keyword(s):  
Sato Grassmannian ◽  
Sigma Function

Relationship between the prime form and the sigma function for some cyclic (r,s) curves

2013 ◽  
Vol 46 (17) ◽  
pp. 175203 ◽  
Author(s):  
John Gibbons ◽  
Shigeki Matsutani ◽  
Yoshihiro Ônishi
Keyword(s):  
Sigma Function ◽  
Prime Form
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