scholarly journals Numerical Evaluation of Elliptic Functions, Elliptic Integrals and Modular Forms

2019 ◽  
pp. 269-293 ◽  
Author(s):  
Fredrik Johansson
Keyword(s):  
Modular Forms ◽  
Numerical Evaluation ◽  
Elliptic Functions ◽  
Elliptic Integrals

scholarly journals EXCEPTIONAL STRING: INSTANTON EXPANSIONS AND SEIBERG–WITTEN CURVE

2002 ◽  
Vol 14 (09) ◽  
pp. 913-975 ◽  
Author(s):  
KENJI MOHRI
Keyword(s):  
Modular Forms ◽  
Mirror Symmetry ◽  
Elliptic Functions ◽  
Partition Functions ◽  
String Models ◽  
Local Mirror Symmetry

We investigate instanton expansions of partition functions of several toric E-string models using local mirror symmetry and elliptic modular forms. We also develop a method to determine the Seiberg–Witten curve of E-string with the help of elliptic functions.

scholarly journals Researches on the geometrical properties of elliptic integrals

1854 ◽  
Vol 6 ◽  
pp. 143-145
Keyword(s):  
Elliptic Integral ◽  
Elliptic Functions ◽  
Second Order ◽  
Elliptic Integrals ◽  
Geometrical Properties ◽  
Entire Class ◽  
The Subject

In this paper the author proposes to investigate the true geometrical basis of that entire class of algebraical expressions, known to mathematicians as elliptic functions or integrals. He sets out by showing what had already been done in this department of the subject by preceding geometers. That the elliptic integral of the second order represented an arc of a plane ellipse, was evident from the beginning.

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