- Title
- New analogues of Clausen’s identities arising from the theory of modular forms
- Creator
- Chan, Heng Huat; Tanigawa, Yoshio; Yang, Yifan; Zudilin, W.
- Relation
- Advances in Mathematics Vol. 228, Issue 2, p. 1294-1314
- Publisher Link
- http://dx.doi.org/10.1016/j.aim.2011.06.011
- Publisher
- Academic Press
- Resource Type
- journal article
- Date
- 2011
- Description
- Around 1828, T. Clausen discovered that the square of certain hypergeometric ₂F₁ function can be expressed as a hypergeometric ₃F₂ function. Special cases of Clausen’s identities were later used by S. Ramanujan in his derivation of 17 series for 1/π. Since then, there were several attempts to find new analogues of Clausen’s identities with the hope to derive new classes of series for 1/π. Unfortunately, none were successful. In this article, we will present three new analogues of Clausen’s identities. Their discovery is motivated by the study of relations between modular forms of weight 2 and modular functions associated with modular groups of genus 0.
- Subject
- Clausen’s identities; modular forms of one variable
- Identifier
- http://hdl.handle.net/1959.13/934806
- Identifier
- uon:11910
- Identifier
- ISSN:0001-8708
- Language
- eng
- Full Text
- Reviewed
- Hits: 1657
- Visitors: 2433
- Downloads: 361
Thumbnail | File | Description | Size | Format | |||
---|---|---|---|---|---|---|---|
View Details Download | ATTACHMENT02 | Author final version | 325 KB | Adobe Acrobat PDF | View Details Download |