Theta-Functions and Modular Equations

1994 ◽  
pp. 138-244
Author(s):  
Bruce C. Berndt
Keyword(s):  
Theta Functions ◽  
Modular Equations

scholarly journals On a pair of Ramanujan’s modular equations and P - Q theta functions of level 35

2019 ◽  
Vol 43 (1) ◽  
pp. 63-80
Author(s):  
Kaliyur Ranganna VASUKI ◽  
Anusha THIPPESHA
Keyword(s):  
Theta Functions ◽  
Modular Equations

ON THE SCHRÖTER FORMULA FOR THETA FUNCTIONS

2009 ◽  
Vol 05 (08) ◽  
pp. 1477-1488 ◽  
Author(s):  
ZHI-GUO LIU ◽  
XIAO-MEI YANG
Keyword(s):  
Theta Function ◽  
Theta Functions ◽  
Modular Equations ◽  
Trigonometric Identity ◽  
Product Identity ◽  
Function Identity ◽  
Special Cases ◽  
Theta Function Identity ◽  
Addition Formulas

The Schröter formula is an important theta function identity. In this paper, we will point out that some well-known addition formulas for theta functions are special cases of the Schröter formula. We further show that the Hirschhorn septuple product identity can also be derived from this formula. In addition, this formula allows us to derive four remarkable theta functions identities, two of them are extensions of two well-known Ramanujan's identities related to the modular equations of degree 5. A trigonometric identity is also proved.

scholarly journals A Note on Certain Modular Equations about Infinite Products of Ramanujan

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Hong-Cun Zhai
Keyword(s):  
Theta Functions ◽  
Modular Equations ◽  
Infinite Products

Ramanujan proposed additive formulae of theta functions that are related to modular equations about infinite products. Employing these formulaes, we derived some identities on infinite products. In the same spirit, we also could present elementary and simple proofs of certain Ramanujan's modular equations on infinite products.

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