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- Title
ON THE SCHRÖTER FORMULA FOR THETA FUNCTIONS.
- Authors
LIU, ZHI-GUO; YANG, XIAO-MEI
- Abstract
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.
- Subjects
THETA functions; ADDITION (Mathematics); MATHEMATICAL formulas; EQUATIONS; TRIGONOMETRIC functions
- Publication
International Journal of Number Theory, 2009, Vol 5, Issue 8, p1477
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042109002754